# QoE-Driven Secure Video Transmission in Cloud-Edge Collaborative Networks

Tantan Zhao, Lijun He, Xinyu Huang, Fan Li  Copyright (c) 2021 IEEE. Personal
use of this material is permitted. However, permission to use this material
for any other purposes must be obtained from the IEEE by sending a request to
<EMAIL_ADDRESS>Manuscript received June 07, 2021; revised August
26, 2021; accepted October 25, 2021. The review of this paper was coordinated
by Prof. Kaigui Bian. This work was supported in part by the National Natural
Science Foundation of China under Grant 62071369 and in part by the Key
Research and Development Program of Shaanxi Province under Grant 2020KW-009.
(Corresponding author: Fan Li.) T. Zhao, L. He, X. Huang and F. Li are with
the Ministry of Education Key Laboratory for Intelligent Networks and Network
Security, School of Information and Communications Engineering, Xi’an Jiaotong
University, Xi’an 710049, China (e-mail: {zhao10111446,
<EMAIL_ADDRESS>{lijunhe, lifan}@mail.xjtu.edu.cn).

###### Abstract

Video transmission over the backhaul link in cloud-edge collaborative networks
usually suffers security risks, which is ignored in most of the existing
studies. The characteristics that video service can flexibly adjust the
encoding rates and provide acceptable encoding qualities, make the security
requirements more possible to be satisfied but tightly coupled with video
encoding by introducing more restrictions on edge caching. In this paper, by
considering the interaction between video encoding and edge caching, we
investigate the quality of experience (QoE)-driven cross-layer optimization of
secure video transmission over the wireless backhaul link in cloud-edge
collaborative networks. First, we develop a secure transmission model based on
video encoding and edge caching. By employing this model as the security
constraint, then we formulate a QoE-driven joint optimization problem subject
to limited available caching capacity. To solve the optimization problem, we
propose two algorithms: a near-optimal iterative algorithm (EC-VE) and a
greedy algorithm with low computational complexity (Greedy EC-VE). Simulation
results show that our proposed EC-VE can greatly improve user QoE within
security constraints, and the proposed Greedy EC-VE can obtain the tradeoff
between QoE and computational complexity.

###### Index Terms:

QoE, cross-layer optimization, wireless backhaul links security, edge caching,
video encoding.

##  I Introduction

With the rapid development of video processing and mobile communication
technology, large numbers of ultra-high-definition (UHD) video-on-demand (VoD)
facing massive links have emerged [1]. The number of video requests is growing
dramatically, which leads to the heavy traffic load of networks and high
latency of users. These factors could bring poor quality of experience (QoE)
for users. Luckily, edge caching (EC) technology, as one of the key
technologies of the cloud-edge collaboration networks in the fifth generation
(5G) system, provides a promising method to handle these challenges [2, 3].
Since EC servers are closer to the users at the network edge and own powerful
intelligent storage capabilities to precache hot videos, massive video
contents can be delivered directly to users from EC servers to reduce backhaul
traffic burden and transmission latency [4, 5, 6]. In addition to transmission
latency, video encoding quality is also a key factor affecting QoE. Video
encoding quality is influenced by video encoding parameters: video encoding
rate. Higher video coding rate means lager total size of the video packets and
will bring higher received video quality. Transmission latency depends on both
video encoding parameters and caching strategy. This is because most of the
transmission time is spent on downloading the uncached video packets over the
backhaul link from MBS. Generally speaking, high video encoding quality and
low transmission latency imply high QoE. While in the practical scenarios with
fixed available caching capacity, too high video encoding quality may result
in too high transmission latency and vice versa. To maximize QoE, we need to
find the tradeoff between video encoding quality and transmission latency by
jointly optimizing video encoding parameters and caching strategy subject to
limited available caching capacity. Therefore, how to balance video encoding
characteristics and edge caching to improve user QoE is worth studying.

Recently, the copyright protection of video is becoming more and more
important. Moreover, the emerging paid VIPs and confidential video services
make the secure transmission of video contents become an issue that cannot be
ignored in cloud-edge collaborative networks. To be specific, for the video
transmission in cloud-edge collaborative networks, when video data is
transmitted from the cloud server to the user in unicast mode, the
eavesdropping user and the legitimate user receive information on the same
frequency channel at the same time. Once channel condition of the eavesdropper
is better than that of the legitimate user, the eavesdropper could
successfully intercept the video packets, which causes data leakage and
infringes on video copyright and benefits of users. Therefore, secure video
transmission is important.

For the transmission security of wireless links from the EC servers to the
users, the existing physical layer secure (PLS) mechanism, which has been
studied intensively and extensively [7, 8, 9, 10], is sufficient. However, the
PLS mechanism is complicated because it could ensure the security of each
video packet. If it is utilized to ensure the transmission security of
wireless backhaul links in the distributed cache scenarios, where an EC server
may be connected to multiple base stations, the system overhead could be
unbearable. Therefore, it is an urgent issue to develop a secure mechanism
with low complexity to ensure secure transmission of wireless backhaul links,
rather than using the strict and complicated traditional PLS mechanism.

The flexible and cost-effective wireless backhaul has become an attractive
alternative to wired backhaul for small cell networks. However, wireless
backhaul is vulnerable to wiretapping due to the intrinsic broadcasting nature
of wireless channels. Therefore, the issue of secure backhaul links has
aroused wide interest of researchers in recent years. Considering unreliable
wireless backhaul connections, the authors in [11] investigated the secrecy
performance of cooperative single carrier HetNets. The authors in [12] studied
the effect of unreliable wireless backhaul links on the secrecy performance of
an energy harvesting relay network. Different transmitter selection schemes
were proposed to enhance the secrecy. Wireless backhaul along with secrecy was
considered for CR network in [13] and [14].

However, most of the existing studies related to secure backhaul links only
analyzed the significant negative impact of the backhaul unreliability on
secure transmission instead of developing methods to enhance the reliability
of wireless backhaul links. Furthermore, the issue of the secure backhaul
links in the cloud-edge collaborative networks is rarely considered. The
authors in [42] considered the security risks of the backhaul links when
studying the optimal cache placement in edge heterogeneous networks.
Nevertheless, the issue aimed at general data transmission, ignoring the
characteristics of the video applications, which resulted in the poor
performance for video transmission applications. Therefore, secure video
transmission through the backhaul links in the cloud-edge collaborative
networks is still an open question.

To address the abovementioned problems in secure video transmission via
backhaul links in cloud-edge collaborative networks, we propose a QoE-driven
cross-layer optimization algorithm to improve video encoding quality, reduce
transmission latency and guarantee security of backhaul links. The main
contributions of this paper can be summarized as follows.

  1. 1.

Problem Formulation of Joint Optimization of Video Encoding and Edge Caching:
Guaranteeing secure video transmission is of equal importance in the cloud-
edge collaborative network besides optimizing QoE. Since video service can
flexibly provide different acceptable encoding qualities to adapt to the real
scenario’s requirements by adjusting the encoding parameters correspondingly,
the extra security requirements can be satisfied with higher possibility but
has to be tightly coupled with video encoding by introducing more restrictions
on edge caching. Therefore, how to find the tradeoff among transmission
latency, video encoding quality and security becomes the new challenge. To
address this issue, we first develop a secure transmission model based on
video encoding and edge caching. By employing this model as the security
constraint, we comprehensively consider the interaction of video encoding and
edge caching and then formulate a QoE-driven joint optimization problem. The
optimization problem aims to optimize both video encoding and caching
strategies simultaneously subject to the limited available caching capacity.

  2. 2.

Near-Optimal and Suboptimal Solutions: The formulated joint optimization
problem is a high-dimension non-linear mixed integer programming problem,
which makes it more difficult to achieve analytical solution. On one hand, the
non-smooth objective function, the non-convex constraints and multiplication
among the optimization variables make the original optimization problem
intractable. On the other hand, the high dimensionality of optimization
variables makes it difficult to obtain the optimal solution. Therefore, we
propose a near-optimal algorithm to solve it. To be specific, efficacious
transformations are performed on the original intractable problem to obtain
its relaxing solution. Then, Boolean bound is developed to obtain the near-
optimal solution by iteration until all Boolean variables are integers.
Furthermore, considering that the near-optimal algorithm is time-consuming, we
also propose a suboptimal algorithm based on the greedy method with low
computational complexity to get the tradeoff between the user QoE and the
computational complexity.

The rest of this paper is organized as follows. Section II reviews the related
works. In Section III, we introduce the system model, which includes the
framework of QoE-driven cross-layer system and describes the secure
transmission model. In Section IV, we formulate the video encoding quality
maximization and latency minimization problem under the secure constraints. In
Section V we propose a near-optimal solution based on joint optimization of
video encoding and edge caching. In Section VI, we propose a suboptimal
solution based on greedy method. Section VII gives the experimental results,
and discusses the performance gains of the proposed algorithms compared to the
existing algorithms. Finally, Section VIII concludes this paper.

##  II Related Work

In this section, we will review and analyze the progress of existing related
work from the following two aspects.

###  II-A QoE-Driven Edge Video Caching

The edge servers are closer to users and have powerful storage capabilities.
By caching multimedia contents during off-peak hours, delay and congestion can
be reduced [15], thereby improving mobile user QoE [16, 17].

To exploit the storage capacity of edge servers, the authors in [18] proposed
a distributed cache optimization algorithm through belief propagation of
heterogeneous networks, which greatly reduced the download delay of users.
From the perspective of the basic information theoretical limit of EC, the
authors in [19] gave the best trade-off between latency and caching.
Considering the particularity of video transmission, the researchers in [20]
proposed a co-caching strategy for small-cell base stations (SBSs) and mobile
devices, which greatly reduced the delay in video content delivery.

In addition to latency, the popularity of video contents also determines
whether the cached videos meet the needs of users. The authors in [21, 22]
proposed a context-aware caching scheme to predict the popularity and learn
the video popularity of a specific context online, which is used to determine
cache replacement strategy. However, with the increasing heterogeneity of user
groups demanding specific video content, the issue of caching mobile video
streaming has become a more complicated task. Therefore, there are also many
papers that use machine learning to predict preferences of users [24, 25, 26,
27, 28].

The studies mentioned above are for traditional video streaming, to improve
the QoE of dynamic adaptive streaming users. The authors in [29] studied the
QoE-driven optimization of EC placement for dynamic adaptive video streaming,
which considers the different rate-distortion characteristics of videos and
the coordination among distributed EC servers. The authors in [30] proposed a
refined caching update strategy based on video popularity, content importance,
and user playback status, which ensured that the video segments to be played
by users could be cached in time. To further improve user QoE, multiple
modules in addition to EC are considered to be optimized comprehensively. The
authors in [31] proposed to enhance the QoE-aware wireless edge caching with
bandwidth provisioning in software-defined wireless networks. Specifically, a
joint optimization mechanism of caching strategy, bandwidth configuration, and
adaptive video streaming was designed to reduce delay and improve QoE. In
addition, the researchers in [32] proposed a joint scheme of caching strategy,
power allocation, user association, and adaptive video streaming to improve
the system spectrum efficiency and user QoE. However, the scheme in [32] will
cause a greater burden on backhaul traffic. Therefore, in [33], the authors
studied the joint optimization scheme of mobile terminal QoE and backhaul
traffic, which reduced power consumption and backhaul traffic, meanwhile
improving QoE. Although the above studies aim to improve the QoE of mobile
users, security issues in the cloud-edge collaborative networks were not
considered.

###  II-B Caching-Based Secure Transmission

With the increasing complexity of network environment, legal transmission in
the networks is inevitably attacked by external malicious nodes, or the SBS
originally used for caching becomes a malicious node and implements
eavesdropping. Therefore, caching-based secure transmission scheme has aroused
wide interest of researchers. The secure schemes proposed by these studies can
be classified as two categories according to different methods used to achieve
security, including encryption and coding based secure schemes and wireless
security mechanism based secure schemes.

For the encryption and coding based secure scheme, in [34], the authors
studied the secure device-to-device coding and caching scheme in the sense of
information theory. The authors in [35] proposed a decentralized secure coding
caching method in wireless ad-hoc networks. The researchers in [36] studied
the attack models in EC systems and proposed lightweight authentication and
secure collaborative caching schemes based on reinforcement learning
techniques for the mobile edge caching. The authors in [37] proposed a secure
caching solution for disaster backup in mobile social networks using fog
computing. In [38], a secure caching scheme in heterogeneous networks for
multi-homing users is designed. A trust mechanism and a Chinese remainder
theorem-based privacy preservation protocol is proposed.

For the wireless security mechanism based secure scheme, in [39], a caching
scheme to enhance PLS for a backhaul-limited cellular network was proposed.
The authors focused on minimizing the transmit power subject to the secrecy
rate, where the backhaul links are considered as wired. In [40], the authors
studied the secure transmission problem in a cache-assisted heterogeneous
networks. To realize the secure and energy-efficient transmission, a joint
cache placement and file delivery scheme was proposed. In [41], the authors
investigated the secure transmission delay minimization problem in an edge
cache-assisted millimeter-wave cloud radio access network. The authors
designed beamforming to minimize the fronthaul transmission delay and access
transmission delay.

Apart from the above studies, for the security risks of backhaul links, the
authors in [42] studied the optimal cache placement problem under secrecy
constraints of backhaul links in edge heterogeneous networks. Specifically,
the authors proposed an edge caching strategy to minimize the average backhaul
links rate and ensure the security of backhaul links. However, what has been
studied in this study is a secure transmission scheme for general data. The
unique characteristics of videos, which allow distortion within acceptable
range, is ignored. Generally speaking, different encoding parameters
correspond to different encoding qualities, which bring different QoE levels.
Therefore, the proposed secure scheme is not specific to video transmission.

##  III SYSTEM MODEL

###  III-A Framework

Figure 1: VoD downlink transmission in cloud-edge collaborative networks.

In this paper, we consider a VoD downlink scenario in the cloud-edge
collaborative networks, where multiple users request video files from the
cloud servers via a macro-cell base station (MBS), which has access to the
cloud servers through wired core network. SBSs are deployed in the coverage
area of the MBS to serve user video requests and communicate with the MBS via
wireless backhaul links. As shown in Fig. 1, the solid red lines denote the
wireless backhaul links between the MBS and SBSs, following[43, 44, 45]. The
number of EC servers is $K$, and let ${\cal K}$ denote the set of $K$ EC
servers and the caching capacity of each EC server is ${\Phi_{k}},\forall
k\in{\cal{K}}$. Each EC server is connected to an SBS. A user requesting video
files is initially served by SBSs. For video services without packet loss, $n$
encoding packets are required to successfully decode video information. If the
number of video packets sent by all EC servers within the connection range is
$m$ and less than $n$, the decoding conditions are not met. Then, the MBS is
contacted to send the remaining $n-m$ video packets to the user via backhaul
links. Based on the above scenario, we propose a QoE-driven joint optimization
scheme of video encoding and edge caching based on the secure transmission
model for the backhaul links, as illustrated in Fig. 2.

Figure 2: QoE-driven joint optimization scheme of video encoding and edge
caching based on secure backhaul links model.

Specifically, the whole block diagram of the joint optimization scheme
contains the modules of MBS, cloud servers, SBSs, EC servers and users. First,
the video encoding information, i.e., encoding rate, QoE model and the
distribution of popularity, from the cloud servers, and the EC information,
i.e., the caching capacity and the number of EC servers from the SBSs, are
sent to the system analysis module MBS. Then, the optimal encoding and caching
strategy based on the collected information and the secure transmission model
of backhaul links are designed by the MBS and sent to the cloud servers and
the SBSs, respectively. The secure transmission model of the backhaul links is
based on video encoding and edge caching. This means that the encoding packet
size, the number of encoding packets cached on the EC servers and the capacity
of EC servers together determine whether the secure transmission can be
achieved. Finally, the video streamings are encoded by the cloud servers
according to the designed encoding strategy and cached on the EC servers
according to the designed caching strategy after being transmitted from the
cloud servers. Here we consider utilizing the adjustable encoding parameters
and the distributed edge cache to avoid data leakage over the wireless
backhaul links from the MBS to the SBSs and construct the secure transmission
model of wireless backhaul links. Based on the secure transmission model, the
QoE-driven joint optimization model of video encoding and edge caching is
established.

###  III-B Secure Transmission Model Based on Video Encoding and Edge Caching

For the high-definition (HD)/UHD VoD services, we assume that there are $F$
original video streamings to be encoded and cached, and let $\cal{F}$ denote
the set of $F$ video streamings. ${p_{j}},\forall j\in{\cal{F}}$ indicates the
requested probability of the $j$-th video file, which is ranked in descending
order according to video popularity. Without loss of generality, we can mark
the most popular video file with index $1$ and the least popular video file
with index $F$. Specifically, the requested probability of a video file can be
described as a Zipf distribution. Assuming that all video files are sorted
according to their popularity, the probability of being requested for each
video file can be obtained by the following formula:

${p_{j}}=\frac{{{1\mathord{\left/{\vphantom{1{{j^{-\theta}}}}}\right.\kern-1.2pt}{{j^{-\theta}}}}}}{{\sum\limits_{j=1}^{F}{{1\mathord{\left/{\vphantom{1{{j^{-\theta}}}}}\right.\kern-1.2pt}{{j^{-\theta}}}}}}},0<\theta<1,\forall
j\in{\cal{F}}$ (1)

where $\theta$ is the tilt factor of the distribution, which is used to
control the distribution of video popularity, and the larger value means that
the requested probability is more concentrated.

To be specific, the following assumptions are made when encoding and caching
video streamings:

  1. 1.

Each video file is encoded into $n$ packets of different sizes, and let
$\cal{N}$ denote the set of $n$ encoding packets. Let ${s_{i,j}}$ denote the
size of the $i$-th video packet of the $j$-th video file. The $n$ video
encoding packets are cached distributedly on different EC servers, following
[31] and [46].

  2. 2.

${\tilde{m}_{k,i,j}}$ denotes whether the $i$-th video packet of the $j$-th
video file is cached on the $k$-th EC server
$\left({{{\tilde{m}}_{k,i,j}}{\rm{=1}}}\right)$ or not
$\left({{{\tilde{m}}_{k,i,j}}{\rm{=0}}}\right)$.

Based on the above assumptions, the cooperative caching strategy among
multiple EC servers can be formulated as a matrix ${{\bf{M}}_{K\times F}}$ of
size $K\times F$, where the rows indicate the EC servers, the columns indicate
the video files, and the element ${m_{k,j}}$ represents the number of encoding
packets of the $j$-th video file cached on the $k$-th EC server, obviously,
${m_{k,j}}=\sum\limits_{i=1}^{n}{{{\tilde{m}}_{k,i,j}}}$. As a result, for
each request, the number of encoding packets of the $j$-th video file that
need to be transmitted through the backhaul links can be expressed as

$R_{j}=n-\min\left({n,\sum\limits_{k=1}^{K}{{m_{kj}}}}\right)$ (2)

Meanwhile, assuming that the number of total requests during the whole
delivery phase received by SBSs is $\Psi$, then the number of requests for the
video file $j$ received by SBSs is ${\Psi_{j}}=\Psi\cdot{p_{j}},\forall
j\in{\cal{F}}$. Therefore, for ${\Psi_{j}}$ requests, the total number of
encoding packets for the $j$-th video file transmitted through the backhaul
links can be obtained as follows:

$\small
P_{j}={\Psi_{j}}\cdot\left[{n-\min\left({n,\sum\limits_{k=1}^{K}{{m_{kj}}}}\right)}\right]$
(3)

For clarity, considering that $n\geq\sum\limits_{k=1}^{K}{{m_{kj}}}$ in our
considered scenario, Eq. (3) can be further formulated as

$\small P_{j}={\Psi_{j}}\cdot\left({n-\sum\limits_{k=1}^{K}{{m_{kj}}}}\right)$
(4)

We know that for the video services without packet loss, secure transmission
can be realized if and only if $P_{j}\leq n-1$. Consequently, the secure
transmission model of backhaul links based on the distributed edge cache can
be expressed by

${\Psi_{j}}\cdot\left({n-\sum\limits_{k=1}^{K}{{m_{kj}}}}\right)\leq n-1$ (5)

After further simplification, we can get

$\sum\limits_{k=1}^{K}{{m_{kj}}}\geq
n\cdot\left({1-\frac{1}{{{\Psi_{j}}}}}\right)+\frac{1}{{{\Psi_{j}}}}$ (6)

Based on the above derivation, we know that the probability of secure
transmission for the requested video is closely related to the encoding
packets cached on EC servers and the number of video requests.

##  IV Problem Formulation

Based on the secure transmission model achieved for backhaul links, the QoE-
driven joint optimization problem of video encoding parameters and edge
caching strategy under the constraints of edge caching capacity and video
encoding rate has been formulated. We define the optimization variables as
${\bf{\tilde{\bf{M}}}}_{K\times n\times
F}=\left\\{{{\tilde{m}}_{k,i,j}},\forall k\in{\cal{K}},\forall
i\in{\cal{N}},\forall j\in{\cal{F}}\right\\}$ and ${\bf{S}}_{n\times
F}=\left\\{{{s}_{i,j}},\forall i\in{\cal{N}},\forall j\in{\cal{F}}\right\\}$,
where ${{{\tilde{m}}_{k,i,j}}}$ and ${{s_{i,j}}}$ denote the caching strategy
and the size of each video encoding packet, respectively. To improve user QoE,
we construct the joint optimization problem expressed by Eq. (7) as follows:

$\displaystyle\mathop{\max}\limits_{{\bf{\tilde{\bf{M}}}},{\bf{S}}}$
$\displaystyle Q\left({\bf{\tilde{\bf{M}}}},{\bf{S}}\right)$ (7a) s.t.
$\displaystyle\sum\limits_{j=1}^{F}{\sum\limits_{i=1}^{n}{{{\tilde{m}}_{k,i,j}}{s_{i,j}}}}\leq{\Phi_{k}},\forall
k\in{\cal{K}}$ (7b)
$\displaystyle\sum\limits_{k=1}^{K}{\sum\limits_{i=1}^{n}{{{\tilde{m}}_{k,i,j}}}}\leq
n,\forall j\in{\cal{F}}$ (7c)
$\displaystyle\sum\limits_{k=1}^{K}{\sum\limits_{i=1}^{n}{{{\tilde{m}}_{k,i,j}}}}\geq
n\cdot\left({1-\frac{1}{{{\Psi_{j}}}}}\right)+\frac{1}{{{\Psi_{j}}}},\forall
j\in{\cal{F}}$ (7d)
$\displaystyle{R_{{{\min}_{j}}}}\leq\frac{{\sum\limits_{i=1}^{n}{{s_{i,j}}}}}{{{T_{d}}}}\leq{R_{{{\max}_{j}}}},\forall
j\in{\cal{F}}$ (7e)
$\displaystyle{{\tilde{m}}_{k,i,j}}\in\left\\{{0,1}\right\\},\forall
k\in{\cal{K}},\forall i\in{\cal{N}},\forall j\in{\cal{F}}$ (7f)

where $Q\left(\cdot\right)$ is the objective function for different
application demands, which can represent a single optimization objective or
the combination of multiple optimization objectives, depending on the
practical application demands. ${R_{{{\min}_{j}}}},\forall j\in{\cal{F}}$ and
${R_{{{\max}_{j}}}},\forall j\in{\cal{F}}$ denote the maximum and minimum
encoding rates of the $j$-th video file, and the larger encoding rate means
the higher QoE. $T_{d}$ denotes the duration of each video file.

To be specific, in our considered VoD downlink scenario, the QoE is determined
by video encoding quality and transmission latency. The optimization objective
is to maximize the video encoding quality and minimize the transmission
latency simultaneously. Then, the $Q\left(\cdot\right)$ can be defined as

$Q\left({\bf{\tilde{\bf{M}}}},{\bf{S}}\right)=\sum\limits_{j=1}^{F}\left[{f\left({{s_{i,j}}}\right)}{\rm{-}}g\left({{{\tilde{m}}_{k,i,j}},{s_{i,j}}}\right)\right],$
(8)

where ${f\left({{s_{i,j}}}\right)}$ denotes the relationship between video
encoding parameters and video encoding quality, which is determined by the
chosen mean opinion score (MOS) model, and
$g\left({{{\tilde{m}}_{k,i,j}},{s_{i,j}}}\right)$ denotes the relationship
among caching strategy, video encoding parameters and transmission latency. In
particular, according to the MOS model in [47], for the $j$-th video file,
${f\left({{s_{i,j}}}\right)}$ and
$g\left({{{\tilde{m}}_{k,i,j}},{s_{i,j}}}\right)$ can be expressed as

$\begin{array}[]{l}{f\left({{s_{i,j}}}\right)}{\rm{=}}C_{1_{j}}\\!\\!\cdot\\!\\!{\left(\\!\\!{\frac{{\sum\limits_{i=1}^{n}\\!\\!{{s_{i,j}}}}}{{{T_{d}}}}}\\!\\!\right)^{3}}\\!\\!\\!\\!\\!+\\!C_{2_{j}}\\!\\!\cdot\\!\\!{\left(\\!\\!{\frac{{\sum\limits_{i=1}^{n}\\!\\!{{s_{i,j}}}}}{{{T_{d}}}}}\\!\\!\right)^{2}}\\!\\!\\!\\!\\!+\\!C_{3_{j}}\\!\\!\cdot\\!\\!\left(\\!\\!{\frac{{\sum\limits_{i=1}^{n}\\!\\!{{s_{i,j}}}}}{{{T_{d}}}}}\\!\\!\right)\\!\\!+\\!C_{4_{j}}\\\
\end{array}$ (9)

where $C_{1_{j}},C_{2_{j}},C_{3_{j}},C_{4_{j}},\forall j\in{{\cal F}}$ are
video encoding quality parameters which can be determined by the encoding rate
range of the $j$-th video file for a given MOS model.

$\begin{array}[]{l}g\left({{{\tilde{m}}_{k,i,j}},{s_{i,j}}}\right)={V_{{}_{j}}}\\!\cdot\\!{\left[{\frac{{{p_{j}}\cdot\left({\sum\limits_{i=1}^{n}{{s_{i,j}}}-\sum\limits_{i=1}^{n}{\sum\limits_{k=1}^{K}{{{\tilde{m}}_{k,i,j}}{s_{i,j}}}}}\right)}}{{{R_{bk}}}}}\right]^{\frac{2}{3}}}\\\
\end{array}$ (10)

where ${V_{{j}}},\forall j\in{{\cal F}}$ is the weighting coefficient of
transmission latency for a given MOS model. ${{R_{bk}}}$ is the transmission
rate of the backhaul links.

Constraint (7b) indicates that the total size of video packets cached in each
EC server should not be greater than the edge caching capacity
${\Phi_{k}},\forall k\in{\cal{K}}$. Constraint (7c) indicates that the number
of video encoding packets cached in all EC servers should not be larger than
the total number of video encoding packets $n$. Constraint (7d) reveals the
number of video encoding packets that need to be cached in EC servers to
ensure the secure transmission of backhaul links. Constraint (7e) gives the
maximum and the minimum limits of encoding rate for each video streaming.
Constraint (7f) denotes caching strategy as the binary variables, which means
whether the $k$-th EC server caches the $i$-th packet of the $j$-th video file
or not.

By observing the formulated optimization problem in Eq. (7), we can know that
caching strategy and video encoding parameters cooperatively affect the
security of the transmission. Specifically, the security constraint in Eq.
(7d) acts on caching strategy, meanwhile Eq. (7b) reveals that the video
encoding parameters interact with caching strategy. Thus, security constraint
in Eq. (7d) actually acts on caching strategy and video encoding parameters
simultaneously. When the capacity of EC server is limited and security
constraint is strict, video encoding parameters and caching strategy can be
jointly optimized and cooperatively adjusted to ensure security. More video
encoding packets could be cached on EC server in proper encoding rate to
satisfy the secure constraint and the limited edge caching capacity.

##  V Near Opimal Solution Based on Joint Optimization of Video Encoding and
Edge Caching

The optimization problem formulated in section IV is an intractable problem.
Because it is a high-dimension non-linear mixed 0-1 integer programming
problem. First, the non-smooth objective function and the non-convex
constraints make the original optimization problem intractable. Furthermore,
the multiplication and coupling among the high-dimension optimization
variables make the original optimization problem even more intractable.
Finally, the high dimensionality of optimization variables make it difficult
to obtain the optimal solution of the original optimization problem. To solve
it, a near-optimal solution based on relaxation and Boolean bound is proposed
in this subsection. Specifically, the whole solving procedure can be divided
into two steps, i.e., relaxation of the original high-dimension non-linear
mixed 0-1 integer programming problem and the near-optimal solution based on
the derived Boolean bound. In the following section of this paper, we will
describe them in detail.

###  V-A Relaxation of the Original High-Dimension Non-linear Mixed 0-1
Integer Problem

We first relax the original mixed 0-1 integer programming problem with integer
constraints into the relaxing problem without integer constraints. Then, the
relaxing solution of the relaxing problem can be obtained by utilizing
GlobalSearch. We can easily get the relaxing problem, which can be expressed
by the following:

$\displaystyle\mathop{\max\\!}\limits_{{\bf{\tilde{\bf{M}}}},{\bf{S}}}$
$\displaystyle\sum\limits_{j=1}^{F}\left[{f\left({{s_{i,j}}}\right)}{\rm{-}}g\left({{{\tilde{m}}_{k,i,j}},{s_{i,j}}}\right)\right]$
(11a) s.t. $\displaystyle\;\eqref{7b},\eqref{7c},\eqref{7d},\eqref{7e}$ (11b)
$\displaystyle 0\leq{\tilde{m}_{k,i,j}}\leq 1,\forall k\in{{\cal K}},\forall
i\in{{\cal N}},\forall j\in{{\cal F}}$ (11c)

Particularly, the relaxing processing is based on the fact that the optimal
solution of the mixed integer programming, denoted as
${\bf{\tilde{\bf{M}}}}_{opt}$ and ${\bf{S}}_{opt}$, will not be superior to
the optimal solution of its relaxing problem, which is the upper bound of the
original mixed integer programming. Here, the definition of the relaxing
problem can be expressed as: the objective function and remaining constraints
of the original mixed integer programming problem without considering the
integer constraint (7f), which is replaced by continuous range constraint
(11c).

The relaxing problem (11) above is a maximization problem, which is obtained
by replacing the integer constraint (7f) in the original mixed 0-1 integer
programming problem (7) with the continuous range constraint (11c) in the
relaxing problem (11). For this maximization problem, as a typical
reformulation method for solving optimization problem, we consider a
minimization problem equivalent to the maximization problem (11) as follows:

$\displaystyle\mathop{\min}\limits_{{\bf{\tilde{\bf{M}}}},{\bf{S}}}$
$\displaystyle\sum\limits_{j=1}^{F}\left[g\left({{{\tilde{m}}_{k,i,j}},{s_{i,j}}}\right){\rm{-}}{f\left({{s_{i,j}}}\right)}\right]$
(12a) s.t.
$\displaystyle\;\eqref{7b},\eqref{7c},\eqref{7d},\eqref{7e},\eqref{11c}$ (12b)

The minimization problem (12) is actually a non-linear optimization problem.
Therefore, we consider utilizing the global optimal algorithm GlobalSearch
provided by Global Optimization Toolbox of MATLAB to obtain its solution.
Actually, the near-optimal solution of optimization problem (12) can be
obtained by the use of GlobalSearch algorithm, which is a kind of heuristic
search algorithm. We can denote the near-optimal solution of relaxing problem
(12) as ${\bf{\tilde{\bf{M}}}}_{r}$ and ${\bf{S}}_{r}$, and the corresponding
objective function value is $Q_{r}$.

###  V-B Near-Optimal Solution Employing Boolean Bound

To obtain the near-optimal solution of the original mixed integer programming,
we employ the branch and bound method [48]. Specifically, we can discuss the
solution of the relaxing problem (12) in two cases.

In case one, the solution in ${\bf{\tilde{\bf{M}}}}_{r}$ concerning integer-
variables ${\bf{\tilde{\bf{M}}}}_{K\times n\times
F}=\left\\{{{\tilde{m}}_{k,i,j}},\forall k\in{\cal{K}},\forall
i\in{\cal{N}},\forall j\in{\cal{F}}\right\\}$ are integers. Then, the near-
optimal solution ${\bf{\tilde{\bf{M}}}}_{r}$ and ${\bf{S}}_{r}$ of the
relaxing problem is also the near-optimal solution of the original non-linear
mixed optimization problem and the near-optimal solution is obtained as
${\bf{\tilde{\bf{M}}}}_{opt}={\bf{\tilde{\bf{M}}}}_{r}$,
${\bf{S}}_{opt}={\bf{S}}_{r}$.

In case two, an element of solution ${\bf{\tilde{\bf{M}}}}_{r}$ concerning
integer-variables ${\bf{\tilde{\bf{M}}}}_{K\\!\times n\times
F}\\!=\\!\left\\{{{\tilde{m}}_{k,i,j}},\forall k\in{\cal{K}},\forall
i\\!\in{\cal{N}},\forall j\\!\in{\cal{F}}\right\\}$ is not integer. Then, the
non-integer element should be branched. The whole procedure of branching can
be divided into the following three steps:

  * •

Deriving Boolean Bound

The integer variable ${{\tilde{m}}_{k^{\prime},i^{\prime},j^{\prime}}},\forall
k^{\prime}\in{\cal{K}},\forall i^{\prime}\in{\cal{N}},\forall
j^{\prime}\in{\cal{F}}$ is actually called Boolean variable. The near-optimal
solution ${\bf{\tilde{\bf{M}}}}_{opt}$ can be initialized as
${\bf{\tilde{\bf{M}}}}_{opt}={\bf{\tilde{\bf{M}}}}_{r}$. Without loss of
generality, in our non-linear mixed integer optimization problem to be solved,
we use ${{\tilde{m}}_{k^{\prime},i^{\prime},j^{\prime}}},\forall
k^{\prime}\in{\cal{K}},\forall i^{\prime}\in{\cal{N}},\forall
j^{\prime}\in{\cal{F}}$ to denote the Boolean variable which does not satisfy
the integer constraint and ${b_{k^{\prime},i^{\prime},j^{\prime}}},\forall
k^{\prime}\in{\cal{K}},\forall i^{\prime}\in{\cal{N}},\forall
j^{\prime}\in{\cal{F}}$ to denote its corresponding non-integer solution.
Specifically, branch means that the relaxing problem (12) obtained from the
original non-linear mixed integer problem should be further relaxed into two
new sub-relaxing problems, which can be named sub-relaxing problem one and
sub-relaxing problem two. Relaxing means adding two inequality constraints
concerning Boolean variable
${{\tilde{m}}_{k^{\prime},i^{\prime},j^{\prime}}},\forall
k^{\prime}\in{\cal{K}},\forall i^{\prime}\in{\cal{N}},\forall
j^{\prime}\in{\cal{F}}$ to the relaxing problem (12) and keeping its original
objective function and remaining constraints. To be specific, for the sub-
relaxing problem one, the added inequality constraint can be expressed as
${{\tilde{m}}_{k^{\prime},i^{\prime},j^{\prime}}}\leq\left\lfloor{{b_{k^{\prime},i^{\prime},j^{\prime}}}}\right\rfloor,\forall
k^{\prime}\in{\cal{K}},\forall i^{\prime}\in{\cal{N}},\forall
j^{\prime}\in{\cal{F}}$, while for the sub-relaxing problem two, the added
inequality constraint is
${{\tilde{m}}_{k^{\prime},i^{\prime},j^{\prime}}}\geq\left\lfloor{{b_{k^{\prime},i^{\prime},j^{\prime}}}}\right\rfloor+1,\forall
k^{\prime}\in{\cal{K}},\forall i^{\prime}\in{\cal{N}},\forall
j^{\prime}\in{\cal{F}}$, where $\left\lfloor\cdot\right\rfloor$ means rounding
down.

It can be observed that, the added inequality constraint
${{\tilde{m}}_{k^{\prime},i^{\prime},j^{\prime}}}\leq\left\lfloor{{b_{k^{\prime},i^{\prime},j^{\prime}}}}\right\rfloor,\forall
k^{\prime}\in{\cal{K}},\forall i^{\prime}\in{\cal{N}},\forall
j^{\prime}\in{\cal{F}}$ for the sub-relaxing problem one can combine with Eq.
(11c) and merge into one equality constraint. Hence, the inequality constraint
${{\tilde{m}}_{k^{\prime},i^{\prime},j^{\prime}}}\leq\left\lfloor{{b_{k^{\prime},i^{\prime},j^{\prime}}}}\right\rfloor,\forall
k^{\prime}\in{\cal{K}},\forall i^{\prime}\in{\cal{N}},\forall
j^{\prime}\in{\cal{F}}$ in the sub-relaxing problem one can be equivalently
transformed into equality constraint
${{\tilde{m}}_{{k^{\prime},i^{\prime},j^{\prime}}}}=0,\forall
k^{\prime}\in{\cal{K}},\forall i^{\prime}\in{\cal{N}},\forall
j^{\prime}\in{\cal{F}}$, which is called Boolean bound of 0 branch. Similarly,
the added inequality constraint
${{\tilde{m}}_{k^{\prime},i^{\prime},j^{\prime}}}\geq\left\lfloor{{b_{k^{\prime},i^{\prime},j^{\prime}}}}\right\rfloor+1,\forall
k^{\prime}\in{\cal{K}},\forall i^{\prime}\in{\cal{N}},\forall
j^{\prime}\in{\cal{F}}$ for the sub-relaxing problem two can combine with Eq.
(11c) and merge into one equality constraint. Therefore, the inequality
constraint
${{\tilde{m}}_{k^{\prime},i^{\prime},j^{\prime}}}\geq\left\lfloor{{b_{k^{\prime},i^{\prime},j^{\prime}}}}\right\rfloor+1,\forall
k^{\prime}\in{\cal{K}},\forall i^{\prime}\in{\cal{N}},\forall
j^{\prime}\in{\cal{F}}$ in the sub-relaxing problem two can be equivalently
transformed into the equality constraint
${{\tilde{m}}_{k^{\prime},i^{\prime},j^{\prime}}}=1,\forall
k^{\prime}\in{\cal{K}},\forall i^{\prime}\in{\cal{N}},\forall
j^{\prime}\in{\cal{F}}$, which is called Boolean bound of 1 branch.

  * •

Formulating Two Sub-relaxing Problems

Based on the obtained minimization relaxing problem (12) and Boolean bound of
the 0-1 branches, we can easily get the sub-relaxing problem one and sub-
relaxing problem two as follows:

Sub-relaxing problem one:

$\displaystyle\mathop{\min}\limits_{{\bf{\tilde{\bf{M}}}},{\bf{S}}}$
$\displaystyle\sum\limits_{j=1}^{F}\left[g\left({{{\tilde{m}}_{k,i,j}},{s_{i,j}}}\right){\rm{-}}{f\left({{s_{i,j}}}\right)}\right]$
(13a) s.t. $\displaystyle\;\eqref{7b},\eqref{7c},\eqref{7d},\eqref{7e}$ (13b)
$\displaystyle{{\tilde{m}}_{k^{\prime},i^{\prime},j^{\prime}}}=0,\forall
k^{\prime}\in{\cal{K}},\forall i^{\prime}\in{\cal{N}},\forall
j^{\prime}\in{\cal{F}}$ (13c)

where constraint (13c) is the Boolean bound of 0 branch for the Boolean
variable ${{\tilde{m}}_{k^{\prime},i^{\prime},j^{\prime}}},\forall
k^{\prime}\in{\cal{K}},\forall i^{\prime}\in{\cal{N}},\forall
j^{\prime}\in{\cal{F}}$.

Sub-relaxing problem two:

$\displaystyle\mathop{\min}\limits_{{\bf{\tilde{\bf{M}}}},{\bf{S}}}$
$\displaystyle\sum\limits_{j=1}^{F}\left[g\left({{{\tilde{m}}_{k,i,j}},{s_{i,j}}}\right){\rm{-}}{f\left({{s_{i,j}}}\right)}\right]$
(14a) s.t. $\displaystyle\;\eqref{7b},\eqref{7c},\eqref{7d},\eqref{7e}$ (14b)
$\displaystyle{{\tilde{m}}_{k^{\prime},i^{\prime},j^{\prime}}}=1,\forall
k^{\prime}\in{\cal{K}},\forall i^{\prime}\in{\cal{N}},\forall
j^{\prime}\in{\cal{F}}$ (14c)

where constraint (14c) is the Boolean bound of 1 branch for the Boolean
variable ${{\tilde{m}}_{k^{\prime},i^{\prime},j^{\prime}}},\forall
k^{\prime}\in{\cal{K}},\forall i^{\prime}\in{\cal{N}},\forall
j^{\prime}\in{\cal{F}}$.

  * •

Obtaining Near-Optimal Solution

The sub-relaxing problem one formulated in Eq. (13) and the sub-relaxing
problem two formulated in Eq. (14) can also be solved by GlobalSearch
algorithm due to the fact that their forms are similar to the minimization
relaxing problem (12).

There are only two possible solutions for the two sub-relaxing problems
expressed by Eq. (13) and Eq. (14), i.e., infeasible solution and integer
solution due to the Boolean bound of 0-1 branches. For the convenience of
solving the problem, if the infeasible solution appears for the sub-relaxing
problem, we can directly set it as positive infinity or negative infinity,
which depends on whether the relaxing problem is a maximization problem or a
minimization problem. Then, the near-optimal solution for one iteration of 0-1
branch and bound can be obtained by comparing the objective function values of
two sub-relaxing problems to find the minimization branch and its
corresponding solution, denoted as ${\bf{\tilde{\bf{M}}}}_{min}$ and
${\bf{S}}_{min}$, which are used to update the near-optimal solution
${\bf{\tilde{\bf{M}}}}_{opt}$ and ${\bf{S}}_{opt}$ for each iteration by
letting ${\bf{\tilde{\bf{M}}}}_{opt}={\bf{\tilde{\bf{M}}}}_{min}$ and
${\bf{S}}_{opt}={\bf{S}}_{min}$.

A new non-integer solution may appear in the updated solution
${\bf{\tilde{\bf{M}}}}_{opt}$ due to the 0-1 branch and bound. Therefore, if
there is still one non-integer solution in the obtained
${\bf{\tilde{\bf{M}}}}_{opt}$, the 0-1 branch and bound should be executed
continually based on the sub-relaxing problems formulated in Eq. (13) and Eq.
(14). To be specific, Boolean bound concerning the new non-integer solution
should be added to the sub-relaxing problems (13) and (14). Then, the near-
optimal solution ${\bf{\tilde{\bf{M}}}}_{opt}$ and ${\bf{S}}_{opt}$ can be
obtained by updating them as the near-optimal solution of the minimization
branch of the current iteration of 0-1 branch and bound. Finally, the near-
optimal solution of the original non-linear mixed integer optimization problem
can be obtained until there is no non-integer solution in the updated near-
optimal solution ${\bf{\tilde{\bf{M}}}}_{opt}$. The corresponding objective
function value $Q_{min}$ can be obtained by substituting the near-optimal
solution ${\bf{\tilde{\bf{M}}}}_{opt}$ and ${\bf{S}}_{opt}$ into the objective
function of the optimization problem (12).

Generally speaking, to obtain the near-optimal integer solution of the
considered optimization problem formulated in Eq. (12), the maximum iteration
to execute 0-1 branch and bound is $K\cdot n\cdot F$, which is actually the
number of elements in the three-dimensional integer variable
${\bf{\tilde{\bf{M}}}}_{K\times n\times
F}=\left\\{{{\tilde{m}}_{k,i,j}},\forall k\in{\cal{K}},\forall
i\in{\cal{N}},\forall j\in{\cal{F}}\right\\}$. Particularly, for each
iteration of the 0-1 branch and bound, if there is more than one non-integer
element, denoted as $N_{n},{N_{n}}\geq 2$, in the updated solution
${\bf{\tilde{\bf{M}}}}_{opt}$, 0-1 branch and bound should be executed for
each non-integer solution. Then, $2\cdot{N_{n}}$ branches are generated, which
are compared to find the minimization branch and its corresponding solution
${\bf{\tilde{\bf{M}}}}_{min}$ and ${\bf{S}}_{min}$ to update the near-optimal
solution as ${\bf{\tilde{\bf{M}}}}_{opt}={\bf{\tilde{\bf{M}}}}_{min}$,
${\bf{S}}_{opt}={\bf{S}}_{min}$.

The solving procedure of our proposed near-optimal algorithm is summarized in
Algorithm 1 named Near-Optimal Algorithm Based on Relaxation and Boolean
bound.

Input: $myfun1$: the objective function of optimzaton problem (12); $myfun2$:
non-linear constraints of optimization problem (12); linear constraints of
optimization problem (12); ${\bf{\tilde{\bf{M}}}}_{0}$, $\bf{S}_{0}$: initial
solution of ${\bf{\tilde{\bf{M}}}}$ and $\bf{S}$.

Output: ${\bf{\tilde{\bf{M}}}}_{opt}$, ${\bf{S}}_{opt}$ and $Q_{min}$.

Initialize: Obtain ${\bf{\tilde{\bf{M}}}}_{r}$, $\bf{S}_{r}$ and the objective
function value $Q_{r}$ by solving relaxing problem (12). Calculate the initial
total number of non-integer elements in ${\bf{\tilde{\bf{M}}}}_{r}$, denoted
as $N_{n}$, and obtain the position index ${{\bf{N}}_{in}}$. Initialize the
left coefficient matrix of equality constraints (13c) in Eq. (13) and (14c) in
Eq. (14) as ${{\bf{A}}_{eq}}={\bf{0}}$, and the right coefficient vector of
equality constraints as ${{\bf{b}}_{eq}}={\bf{0}}$.

if  _$N_{n}$ = 0_ then

${\bf{\tilde{\bf{M}}}}_{opt}$ = ${\bf{\tilde{\bf{M}}}}_{r}$;

${\bf{S}}_{opt}={\bf{S}}_{r}$;

$Q_{min}$ = $Q_{r}$;

else

Initialzie ${\bf{\tilde{\bf{M}}}}_{opt}$ = ${\bf{\tilde{\bf{M}}}}_{r}$. Set
the number of non-integer solution in ${\bf{\tilde{\bf{M}}}}_{opt}$ for each
iteration of 0-1 branch and bound as $N_{b}$ = $N_{n}$ and the corresponding
position index vector ${{\bf{N}}_{i}}$ = ${{\bf{N}}_{in}}$.

for  _$p=1$ to $N_{n}$_ do

for  _$q=1$ to $N_{b}$_ do

Update ${{\bf{A}}_{eq}}\left({p,{{\bf{N}}_{i}}\left({:,q}\right)}\right)=1$;

Obtain the left coefficient matrix of equality constraints for 0 and 1 branch
${{\bf{A}}_{eq\\_zero}}={{\bf{A}}_{eq}}\left({1:p,:}\right)$,
${{\bf{A}}_{eq\\_one}}={{\bf{A}}_{eq}}\left({1:p,:}\right)$;

Update ${{\bf{b}}_{eq}}\left({p,:}\right)=0$;

Obtain the right coefficient vector of equality constraints for 0 branch
${{\bf{b}}_{eq\\_zero}}={{\bf{b}}_{eq}}\left({1:p,:}\right)$;

Update ${{\bf{b}}_{eq}}\left({p,:}\right)=1$;

Obtain the right coefficient vector of equality constraints
${{\bf{b}}_{eq\\_one}}={{\bf{b}}_{eq}}\left({1:p,:}\right)$;

Solving the sub-relaxing problem one (13) and the sub-relaxing problem two
(14) by utilizing the global optimal algorithm GlobalSearch.

end for

Compare the objective function values of all 0-1 branches of $N_{b}$ non-
integer variables, and find the minimization branch and obtain its
corresponding solution, denoted as ${\bf{\tilde{\bf{M}}}}_{min}$ and
${\bf{S}}_{min}$;

Update ${\bf{\tilde{\bf{M}}}}_{opt}$ by setting
${\bf{\tilde{\bf{M}}}}_{opt}={\bf{\tilde{\bf{M}}}}_{min}$,
${\bf{S}}_{opt}={\bf{S}}_{min}$;

Update $N_{b}$ and ${{\bf{N}}_{i}}$ based on ${\bf{\tilde{\bf{M}}}}_{opt}$.

end for

Obtain ${\bf{\tilde{\bf{M}}}}_{opt}$, ${\bf{S}}_{opt}$ and the objective
function value $Q_{min}$ by substituting ${\bf{\tilde{\bf{M}}}}_{opt}$ and
${\bf{S}}_{opt}$ into the objective function $myfun1$ of optimization problem
(12).

end if

Algorithm 1 Near-Optimal Algorithm Based on Relaxation and Boolean bound

##  VI Suboptimal Solution Based on Greedy Method

Considering that the near-optimal algorithm proposed is time-consuming, we
propose a greedy algorithm with low computational complexity to obtain the
suboptimal solution of original non-linear mixed 0-1 integer programming
problem. The main idea of the greedy algorithm is to optimize variables
${\bf{\tilde{\bf{M}}}}=\left\\{{{\tilde{m}}_{k,i,j}},\forall
k\in{\cal{K}},\forall i\in{\cal{N}},\forall j\in{\cal{F}}\right\\}$ and
${\bf{\bf{S}}}=\left\\{{{\tilde{s}}_{i,j}},\forall i\in{\cal{N}},\forall
j\in{\cal{F}}\right\\}$ separately. The whole procedure is presented in the
following two subsections.

###  VI-A Caching Strategy Optimization with Encoding Parameters Fixed

First, we optimize variable ${\bf{\tilde{\bf{M}}}}_{K\times n\times
F}=\left\\{{{\tilde{m}}_{k,i,j}},\forall k\in{\cal{K}},\forall
i\in{\cal{N}},\forall j\in{\cal{F}}\right\\}$ with the encoding parameters
fixed. The solution of variable ${\bf{\tilde{\bf{M}}}}_{K\times n\times
F}=\left\\{{{\tilde{m}}_{k,i,j}},\forall k\in{\cal{K}},\forall
i\in{\cal{N}},\forall j\in{\cal{F}}\right\\}$ can be obtained by solving the
optimization problem (7) under the condition of giving the variable
${\bf{\bf{S}}}=\left\\{{{\tilde{s}}_{i,j}},\forall i\in{\cal{N}},\forall
j\in{\cal{F}}\right\\}$ a fixed value according to a given encoding rate.
Actually, the solving process is the special case of Algorithm 1 with a fixed
known ${{\bf{S}}}$, which greatly reduces the complexity of solving the
optimization problem compared with a variable ${{\bf{S}}}$ since the dimension
of the optimization variable reduces.

According to Algorithm 1, with a fixed known ${{\bf{S}}}$, the optimization
problem (12), (13) and (14) should be changed accordingly. Specifically, the
minimization relaxing problem (12) can be reformulated as

$\displaystyle\mathop{\min}\limits_{{\bf{\tilde{\bf{M}}}}}$
$\displaystyle\sum\limits_{j=1}^{F}g\left({{{\tilde{m}}_{k,i,j}}}\right)$
(15a) s.t. $\displaystyle\;\eqref{7b},\eqref{7c},\eqref{7d},\eqref{11c}$ (15b)

Based on the reformulated minimization relaxing problem (15), the sub-relaxing
problem one (13) and sub-relaxing problem two (14) can be reformulated as

Sub-relaxing problem one:

$\displaystyle\mathop{\min}\limits_{{\bf{\tilde{\bf{M}}}}}$
$\displaystyle\sum\limits_{j=1}^{F}g\left({{{\tilde{m}}_{k,i,j}}}\right)$
(16a) s.t. $\displaystyle\;\eqref{7b},\eqref{7c},\eqref{7d},\eqref{13c}$ (16b)

Sub-relaxing problem two:

$\displaystyle\mathop{\min}\limits_{{\bf{\tilde{\bf{M}}}}}$
$\displaystyle\sum\limits_{j=1}^{F}g\left({{{\tilde{m}}_{k,i,j}}}\right)$
(17a) s.t. $\displaystyle\;\eqref{7b},\eqref{7c},\eqref{7d},\eqref{14c}$ (17b)

###  VI-B Encoding Parameters Optimization Based on the Greedy Method

Then, based on the caching strategy ${{\bf{\tilde{M}}}_{g}}$ obtained, the
solution of variable ${\bf{\bf{S}}}=\left\\{{{\tilde{s}}_{i,j}},\forall
i\in{\cal{N}},\forall j\in{\cal{F}}\right\\}$ can be obtained as
${{\bf{S}}_{g}}$ by gradually increasing the encoding rate for each video file
one by one in a certain reasonable step. In this way, we can find the one
which brings the maximum MOS value of the current iteration until not meeting
the constraints in the optimization problem (12).

Finally, the suboptimal solution of the original non-linear mixed non-integer
solution can be obtained as ${{\bf{\tilde{M}}}_{g}}$ and ${{\bf{S}}_{g}}$. The
corresponding objective function value $Q_{min}$ can be obtained by
substituting the suboptimal solution ${{\bf{\tilde{M}}}_{g}}$ and
${{\bf{S}}_{g}}$ into the objective function of the optimization problem (12).
The solving procedure for the greedy algorithm is summarized in Algorithm 2
named Suboptimal Algorithm Based on Greedy Method.

Input: Caching strategy ${{\bf{\tilde{M}}}_{g}}$, which is obtained by
utilizing Algorithm 1 with the known ${\bf{S}}$ based on the given encoding
rate which satisfies constraint (7d) in optimization problem (12).

Output: ${{\bf{\tilde{M}}}_{g}}$, ${\bf{S}}_{g}$ and $Q_{min}$.

Initialize: initialize ${\bf{S}}_{g}$ according to the minimum encoding rates;
initialize $Q_{min}$ as $Q_{min}=Q_{g}$ which is calculated based on the
obtained ${\bf{\tilde{\bf{M}}}}_{g}$ and ${\bf{S}}_{g}$; initialize increasing
step of encoding rate as $\frac{1}{{{T_{d}}\cdot n}}$; initialize the
searching times $N_{1}$ and $N_{2}$ as
${N_{1}}=\left({{R_{\max}}-{R_{\min}}}\right)\cdot{T_{d}}\cdot N$,
${N_{2}}=F$, where $N$ is the number of video files whose encoding rate lies
between ${R_{\min}}$ and ${R_{\max}}$.

for  _$p=1$ to $N_{1}$_ do

for  _$q=1$ to $N_{2}$_ do

Obtain all possible ${\bf{S}}_{g}$ which satisfy constraints in optimization
problem (12) according to the increasing step $\frac{1}{{{T_{d}}\cdot n}}$.

Obtain all possible $Q_{g}$ by substituting all possible ${\bf{S}}_{g}$,
${{\bf{\tilde{M}}}_{g}}$ into the objective function of optimization problem
(12).

end for

Compare all possible $Q_{g}$ and find the one which brings the most increments
to $Q_{min}$, denoted as $Q_{gmin}$ and its corresponding encoding parameters,
denoted as ${{\bf{S}}_{g\min}}$.

Update ${\bf{S}}_{g}$ by setting ${\bf{S}}_{g}={{\bf{S}}_{g\min}}$;

Update $Q_{min}$ by setting $Q_{min}=Q_{gmin}$.

end for

Algorithm 2 Suboptimal Algorithm Based on Greedy Method

##  VII Simulation Results

In this section, we provide simulation results to highlight the performance of
our algorithms. We consider a VoD downlink scenario in the cloud-edge network
where the total number of video files is $F$, the total encoding packet of
each video file is $n$, and the number of the EC servers is $K$. The total
number of video requests received by SBSs during the whole delivery phase is
$\psi$. The capacity of EC server is ${\Phi_{k}},\forall k\in K$. To reveal
the performance of the proposed algorithms in scenarios with different
configuration, the parameters $F,n,K,\psi,{\Phi_{k}}$ can be adjusted in
different figures. The tilt factor of the Zipf distribution is assumed as
$\theta=0.8$ referring to relevant work [49, 50]. The duration of each video
file is assumed as $T_{d}=2400s$ because the playback time of a video is
generally 40min to 60min, here we choose 40min. The weighting coefficient of
transmission latency is ${V_{j}}=0.99,\forall j\in{\cal{F}}$ based on the MOS
model in [47]. The transmission rate of the backhaul links is
${R_{bk}}=10{\rm{Gbps/}}F$ according to the 3GPP specification [51]. To verify
that encoding rates can be adjusted adaptively according to different caching
capacity and security constraints, files of different encoding rates are
considered. In particular, we consider three types of video files, the
encoding rates of which satisfy different encoding rate ranges:

Type 1: The encoding rates of the 1st to the ($2/F$)-th video files vary from
0.3 Mbps to 0.7 Mbps;

Type 2: The encoding rates of the (${2/F}+1$)-th to the (${2/F}+{4/F}$)-th
video files vary from 1Mbps to 4 Mbps;

Type 3: The encoding rates of the (${2/F}+{4/F}+1$)-th to the $F$-th video
files vary from 4 Mbps to 8 Mbps.

The detailed parameter settings are presented in Table I. Our proposed schemes
and three existing algorithms are presented and analyzed as follows:

  * •

EC-VE (Edge Caching and Video Encoding): Our proposed near-optimal edge
caching and video encoding based algorithm that jointly optimizes video
encoding parameters and edge caching strategy.

  * •

Greedy EC-VE (Greedy Edge Caching and Video Encoding): Our proposed greedy
edge caching and video encoding based algorithm with lower complexity, which
optimizes video encoding parameters and edge caching strategy step by step.

  * •

ECST (Edge Caching Secure Transmission) in [42]: The edge caching based secure
transmission scheme aims to minimize the backhaul links rate under secrecy
constraints by utilizing edge caching strategy for general data transmission.

  * •

EC-BF (Edge Caching and Beamforming) in [41]: The secure transmission scheme
aims to minimize delay in an edge cache-assisted millimeter-wave cloud radio
access network by designing transmit and receive beamforming.

  * •

EC-TM (Edge Caching and Trust Mechanism) in [38]: The secure caching scheme is
based on a trust mechanism and a Chinese remainder theorem-based privacy
preservation protocol in heterogeneous networks for multi-homing users.

Specifically, we validate the algorithm performance in terms of MOS, average
MOS, transmission latency and the minimum caching capacity to ensure secure
transmission with different simulation configurations. In order to show the
performance difference under different video encoding rates and demonstrate
the important impact of video encoding on system performance, three different
fixed encoding rates are set for video files in the ECST scheme, EC-BF scheme
and EC-TM scheme. In addition, ablation study about video encoding module and
edge caching module is given in subsection VII-G to show the functions of the
two modules and reveal their different effects on system performance. Finally,
the computational complexity of the EC-VE algorithm, greedy EC-VE algorithm,
the ECST algorithm, EC-BF algorithm and EC-TM algorithm is analyzed in
subsection VII-H.

TABLE I: VIDEO FILE PARAMETERS

Types | Encoding rate range | Video encoding quality parameters
---|---|---
Type 1 | 0.3Mbps-0.7Mbps |  |  ${C_{1}}=0.23$, ${C_{2}}=-1.5$,
---
${C_{3}}=3.3$, ${C_{4}}=2.5$
Type 2 | 1Mbps-4Mbps |  |  ${C_{1}}=0.0426$, ${C_{2}}=-0.4466$,
---
${C_{3}}=1.6369$, ${C_{4}}=1.8415$
Type 3 | 4Mbps-8Mbps |  |  ${C_{1}}=0.0027$, ${C_{2}}=-0.0669$,
---
${C_{3}}=0.5842$, ${C_{4}}=2.5248$

Figure 3: (a) MOS of each video file. (b) Average MOS vs. different caching
capacity of EC server.

###  VII-A MOS of Each Video File

Fig. 3. (a) shows the MOS value of each video file with $n=20$, $F=8$, $K=1$
and ${\Phi_{k}}=26880\text{Mb},\forall k\in{\cal{K}}$. The three fixed
encoding rates of video files in the ECST scheme, EC-BF scheme and EC-TM
scheme are ${{R_{\min}}}$,
${R_{\min}}+\left[{{{\left({{R_{\max}}-{R_{\min}}}\right)}\mathord{\left/{\vphantom{{\left({{R_{\max}}-{R_{\min}}}\right)}{10}}}\right.\kern-1.2pt}{10}}}\right]$
and
${R_{\min}}+\left[{{{\left({{R_{\max}}-{R_{\min}}}\right)}\mathord{\left/{\vphantom{{\left({{R_{\max}}-{R_{\min}}}\right)}{20}}}\right.\kern-1.2pt}{20}}}\right]$,
respectively. Fig. 3. (a) shows that, for each video file, the MOS performance
of EC-VE algorithm is not always superior to the MOS performance of other
schemes in spite of the obvious advantage in the average sense. The average
MOS values of the EC-VE algorithm, Greedy EC-VE algorithm, ECST scheme, EC-BF
scheme and EC-TM scheme are 3.7935, 3.4402 and 3.4402, 3.4225 and 3.4110,
respectively. Our optimization goal is the whole performance advantage of all
video files rather than the performance advantage for a single video file.
Thus, there is no absolute superiority of MOS value for each video file in our
proposed algorithm. Specifically, to obtain the whole performance advantage of
the MOS value, the 1-st to 6-th video files, as depicted in Fig. 3. (a), which
can get higher QoE with lower encoding rate, are more likely to be distributed
with caching capacity to improve QoE on the condition of limited caching
capacity, while the 7-th and 8-th video files, which request higher encoding
rate, are distributed with less caching capacity.

Each video file has own caching strategy and encoding parameter. The number
and the size of encoding packets cached on the EC server vary for different
video files. Therefore, the video encoding quality and transmission latency of
each video file are different for the five schemes. This results in different
MOS values in the case of the same caching capacity of the EC server.
Furthermore, the MOS values of the Greedy EC-VE algorithm and ECST scheme are
the same for each video file. This is because each video file of both schemes
is encoded into the minimum encoding rate. Meanwhile, the caching strategy for
each video file is the same when the caching capacity is
${\Phi_{k}}=26880\text{Mb},\forall k\in{\cal{K}}$. This value of caching
capacity allows all encoding packets of each video file to be cached on the EC
server at the minimum encoding rate. Besides, the MOS values of the EC-BF
scheme and the EC-TM scheme are lower than that of the other schemes. Because
for the EC-BF scheme and EC-TM scheme, the secure transmission rate for each
video file is lower than that of other schemes. Moreover, for the EC-TM
scheme, the caching capacity for improving MOS is more scarce compared with
other schemes due to the fact that the encrypted video files are larger and
occupy more caching capacity.

###  VII-B Average MOS with Different Caching Capacity of EC Server

In Fig. 3. (b), the average MOS value versus different caching capacity of EC
server with $n=20$, $F=8$, $K=1$ is presented. The three fixed encoding rates
of video files in the ECST scheme, EC-BF scheme and EC-TM scheme are
${{R_{\min}}}$,
${R_{\min}}+\left[{{{\left({{R_{\max}}-{R_{\min}}}\right)}\mathord{\left/{\vphantom{{\left({{R_{\max}}-{R_{\min}}}\right)}{10}}}\right.\kern-1.2pt}{10}}}\right]$
and
${R_{\min}}+\left[{{{\left({{R_{\max}}-{R_{\min}}}\right)}\mathord{\left/{\vphantom{{\left({{R_{\max}}-{R_{\min}}}\right)}{20}}}\right.\kern-1.2pt}{20}}}\right]$,
respectively. As shown in Fig. 3. (b), the average MOS values of the EC-VE
algorithm and the Greedy EC-VE algorithm increase with the increasing caching
capacity of the EC server. Both of them eventually tend to the same maximum
value, which is determined by the maximum encoding rate of each video file and
the optimal caching strategy. At this time, the caching capacity of EC server
is sufficient to cache all encoding packets. The EC-VE algorithm also achieves
a considerable performance gain compared with the Greedy EC-VE algorithm. The
minimum average MOS value of the proposed EC-VE algorithm is obtained when the
caching capacity of the EC server is just enough to cache the minimum number
of encoding packets to satisfy the security constraints. However, the Greedy
EC-VE algorithm cannot find the feasible solution that satisfies the security
constraints at this point, marked by the purple circle in Fig. 3. (b). As the
caching capacity of the EC server increases, the gap of the average MOS values
is initially large, then gradually narrows. This is because large caching
capacity can provide more choices of caching strategy and encoding rate to
bring better performance on video encoding quality and transmission latency.

Furthermore, the average MOS value of the ECST scheme, which is always worse
than the average MOS value of the proposed EC-VE algorithm and Greedy EC-VE
algorithm, remains unchanged with the increasing caching capacity. This
scenario is reasonable since the minimum encoding rate is adopted in the ECST
scheme. At this time, the caching strategy is the same regardless of the
caching capacity because its aim is to minimize the backhaul links rate. Thus,
the video encoding packets cached on the EC server will be as many as possible
if the caching capacity is large enough and all encoding packets are cached on
the EC server when each video file is encoded into its minimum encoding rate.

Besides, the average MOS values of the EC-BF scheme and the EC-TM scheme,
which are much worse than that of the proposed EC-VE algorithm and Greedy EC-
VE algorithm, increase with the increasing caching capacity initially and
gradually remain stable. In the beginning, less encoding packets are cached on
EC servers to ensure security due to the limited caching capacity. With the
increasing caching capacity, all encoding packets can be cached on EC servers
to ensure security and reduce transmission latency at the same time. However,
the MOS values of the EC-BF scheme and EC-TM scheme keep stable when the
caching capacity continues to increase as a result of the fixed encoding
rates. The gap of the EC-BF scheme and the EC-TM scheme results from different
encoding rate and the effective utilization rate of caching capacity.

The Greedy EC-VE algorithm, the ECST scheme, the EC-BF scheme and the EC-TM
scheme cannot achieve secure transmission when the caching capacity value is
very small, i.e., at the first point marked by the purple circle in Fig. 3.
(b) with caching capacity ${\Phi_{k}}=21540\text{Mb},\forall k\in{\cal{K}}$,
while the proposed EC-VE algorithm can ensure secure transmission and obtain a
feasible average MOS value by adjusting caching strategy and encoding
parameters at the same time. The observations above demonstrate the benefits
of the proposed algorithm, which comprehensively considers the interaction of
caching strategy and encoding parameters, and adjusts both of them
simultaneously to adapt to different caching capacity.

TABLE II: MOS OF EACH VIDEO FILE UNDER DIFFERENT CACHING CAPACITY

MOS of Each Video File under the Smallest Caching Capacity
---
| Index of
---
Video File
1 |  2 |  3 |  4 |  5 |  6 |  7 |  8
| Encoding Rate
---
(Mbps)
0.3 |  0.3 |  0.3 |  0.3 |  1 |  1 |  4 |  4
| Number of
---
Cached Packets
15 |  19 |  17 |  14 |  18 |  18 |  16 |  15
MOS |  3.302 |  3.303 |  3.303 |  3.300 |  2.984 |  2.966 |  2.708 |  2.695
MOS of Each Video File under the Largest Caching Capacity
| Index of
---
Video File
1 |  2 |  3 |  4 |  5 |  6 |  7 |  8
| Encoding Rate
---
(Mbps)
0.7 |  0.7 |  0.7 |  0.7 |  4 |  4 |  8 |  8
| Number of
---
Cached Packets
20 |  20 |  20 |  20 |  20 |  20 |  20 |  20
MOS |  4.116 |  4.116 |  4.116 |  4.116 |  3.932 |  3.932 |  4.261 |  4.261

To show the changes of encoding parameters and caching strategy under
different caching capacity, encoding rates and the number of cached packets
for two selected points in Fig. 3. (b) are given in Table II. At the first
point marked by the purple circle in Fig. 3. (b), the minimum average MOS
value of the proposed EC-VE algorithm is obtained. At the last point marked by
the black circle in Fig. 3. (b), the same maximum average MOS values of the
proposed EC-VE algorithm and Greedy EC-VE algorithm are obtained. Table II
gives the MOS value of each video file at the first point when the EC server
has the smallest caching capacity ${\Phi_{k}}=21540\text{Mb},\forall
k\in{\cal{K}}$ and at the last point when the EC server has the largest
caching capacity ${\Phi_{k}}=69660\text{Mb},\forall k\in{\cal{K}}$. The
minimum MOS of each video file is obtained at the first point. In this
situation, all video files in the EC-VE algorithm are encoded into the minimum
encoding rates, and the minimum number of encoding packets are cached on the
EC server to satisfy the security constraints due to the limited caching
capacity. Meanwhile, the minimum number of cached packets varies for different
video files, because different video files have a different number of
requests. At the last point, the maximum MOS of each video file is obtained,
because all video files of both algorithms are encoded into the maximum
encoding rates and all encoding packets are cached on the EC server due to the
sufficient caching capacity.

###  VII-C Average MOS with Different Parameters of Video Files

Figure 4: (a) Average MOS vs. different number of video files. (b) Average MOS
vs. different number of video encoding packets.

Fig. 4. (a) shows the average MOS value versus different number of video files
with $n=10$, $K=1$ and ${\Phi_{k}}=39000\text{Mb},\forall k\in{\cal{K}}$. The
three fixed encoding rates of video files in the ECST scheme, EC-BF scheme and
EC-TM scheme are
${R_{\min}}+\left[{{{\left({{R_{\max}}-{R_{\min}}}\right)}\mathord{\left/{\vphantom{{\left({{R_{\max}}-{R_{\min}}}\right)}{2}}}\right.\kern-1.2pt}{2}}}\right]$,
${R_{\min}}+\left[{{{\left({{R_{\max}}-{R_{\min}}}\right)}\mathord{\left/{\vphantom{{\left({{R_{\max}}-{R_{\min}}}\right)}{10}}}\right.\kern-1.2pt}{10}}}\right]$
and
${R_{\min}}+\left[{{{\left({{R_{\max}}-{R_{\min}}}\right)}\mathord{\left/{\vphantom{{\left({{R_{\max}}-{R_{\min}}}\right)}{20}}}\right.\kern-1.2pt}{20}}}\right]$,
respectively. From Fig. 4. (a), the average MOS value decreases with the
increasing number of video files for the proposed EC-VE algorithm and the
Greedy EC-VE algorithm. The gap between them increases with the increasing
video files when the number of video files is less than or equal to $F=12$.
However, the Greedy EC-VE algorithm has no solution as the number of video
files continues to increase to $F=16$ and $F=20$, marked by the black and cyan
circles in Fig. 4. (a), while the EC-VE algorithm still has the feasible and
effective solution. Specifically, the minimum average MOS value is obtained at
the last point marked by the cyan circle. At this time, all video files are
encoded into the minimum encoding rates, and the minimum number of encoding
packets are cached on the EC server. Besides, the average MOS values of the
EC-BF scheme and the EC-TM scheme, which are worse than our proposed schemes,
keep stable when the number of video files is less than or equal to $F=8$.
Then, the MOS values of them decrease when the video files increase to $F=12$.

The reasons contributing to these observations are that when there are four
video files, all of them are encoded into the maximum encoding rates in the
proposed near-optimal and greedy algorithm, and encoded into the fixed
encoding rates in the EC-BF scheme and the EC-TM scheme. Meanwhile, all
encoding packets are cached on the EC server due to the sufficient caching
capacity. This brings the best MOS values for each scheme as shown by the
first points. As the number of video files increases, only a part of the
encoding packets can be cached on the EC server due to the limited caching
capacity. This cannot allow all video files to be encoded into the maximum
encoding rates. In this situation, the caching strategy and encoding
parameters of the proposed two algorithms are different. For the EC-VE
algorithm, the near-optimal average MOS value can be obtained by jointly
optimizing the caching strategy and encoding parameters flexibly, while the
Greedy EC-VE algorithm achieves worse MOS values or even an infeasible
solution. The reason is that it optimizes the caching strategy and encoding
parameters step by step. Thus, it cannot satisfy the complex and strict
security constraints when there are many video files. For the EC-BF scheme and
the EC-TM scheme, they cannot ensure security when the video files increase to
$F=12$ because of the fixed encoding rates and limited caching capacity. This
phenomenon further demonstrates the performance advantage of the near-optimal
EC-VE algorithm.

Furthermore, it is interesting to find that there is only one feasible point
marked by the purple circle in Fig. 4. (a) for the ECST scheme when there are
four video files in the considered scenario, and the performance of its
average MOS value is much worse than the proposed algorithms. This is because
the ECST scheme cannot satisfy the security constraints by adjusting its
caching strategy when there are many video files and the caching capacity is
limited. Meanwhile, the simple caching strategy of the ECST scheme demands
that the number of encoding packets cached in different EC servers must be the
same for the same video file.

In Fig. 4. (b), the average MOS value versus different number of video
encoding packets with $F=8$, $K=1$ and ${\Phi_{k}}=28000\text{Mb},\forall
k\in{\cal{K}}$ is presented. The three fixed encoding rates of video files in
the ECST scheme, EC-BF scheme and EC-TM scheme are ${{R_{\min}}}$,
${R_{\min}}+\left[{{{\left({{R_{\max}}-{R_{\min}}}\right)}\mathord{\left/{\vphantom{{\left({{R_{\max}}-{R_{\min}}}\right)}{10}}}\right.\kern-1.2pt}{10}}}\right]$
and
${R_{\min}}+\left[{{{\left({{R_{\max}}-{R_{\min}}}\right)}\mathord{\left/{\vphantom{{\left({{R_{\max}}-{R_{\min}}}\right)}{20}}}\right.\kern-1.2pt}{20}}}\right]$,
respectively. As shown in Fig. 4. (b), the average MOS values of the proposed
EC-VE algorithm, Greedy EC-VE algorithm, the ECST scheme, EC-BF scheme and EC-
TM scheme are almost stable with the increasing number of encoding packets.
The MOS performance of the proposed near-optimal EC-VE algorithm fluctuates
slightly when the number of encoding packets changes. Meanwhile, it is
significantly superior to the Greedy EC-VE algorithm, the ECST scheme, the EC-
BF scheme and EC-TM scheme. Specifically, the MOS performance increases slowly
at first, then decreases when the encoding packets increase to $n=18$, and
finally increases to the maximum value when the number of encoding packets is
$n=20$. The fluctuations result from the caching strategy and the encoding
parameters which vary slightly with the changing total number of encoding
packets, when the caching capacity and the number of video files remain
unchanged. A tradeoff exists between the total number of encoding packets and
the size of each encoding packet, which results in the falling fluctuation
when the number of encoding packets is $n=18$. In this situation, the proposed
near-optimal EC-VE algorithm will wisely consider this balance and achieve the
near-optimal results by joint adjustment of caching strategy and encoding
parameters. This also brings the reasonable fluctuations.

It can also be observed that for the EC-BF scheme and EC-TM scheme, there are
also fluctuations, especially for the EC-BF scheme. This is because the
caching strategy and secure transmission rate adjusts within the available
caching capacity when the number of encoding packets changes, which brings
difference of transmission latency. As for the Greedy EC-VE algorithm, its
performance of the average MOS value is still better than that of the
comparable ECST scheme, while the average MOS values of both schemes almost
remain stable when the number of encoding packets changes. This is because
both of them optimize the caching strategy with the fixed encoding parameters,
which results in the same caching strategy when the caching capacity of the EC
server and the number of video files keep unchanged in spite of the changing
number of total encoding packets.

###  VII-D Average MOS with Different Number of EC Servers

Figure 5: (a) Average MOS vs. different number of EC servers. (b) Transmission
latency vs. different caching capacity of EC server.

Fig. 5. (a) shows the average MOS value versus different number of EC servers
with $n=10,F=12$. The three fixed encoding rates of video files in the ECST
scheme, EC-BF scheme and EC-TM scheme are
${R_{\min}}+\left[{{{\left({{R_{\max}}-{R_{\min}}}\right)}\mathord{\left/{\vphantom{{\left({{R_{\max}}-{R_{\min}}}\right)}{10}}}\right.\kern-1.2pt}{10}}}\right]$,
${R_{\min}}+\left[{{{\left({{R_{\max}}-{R_{\min}}}\right)}\mathord{\left/{\vphantom{{\left({{R_{\max}}-{R_{\min}}}\right)}{2}}}\right.\kern-1.2pt}{2}}}\right]$
and
${R_{\min}}+\left[{{{\left({{R_{\max}}-{R_{\min}}}\right)}\mathord{\left/{\vphantom{{\left({{R_{\max}}-{R_{\min}}}\right)}{5}}}\right.\kern-1.2pt}{5}}}\right]$,
respectively. Considering more general scenarios, EC servers are assumed to
have different caching capacity. To be specific, when the number of EC servers
is $K>1$, the caching capacity values of EC servers are
$[21271\;18272]{\rm{Mb}}$, $[21271\;18272\;13017]{\rm{Mb}}$,
$[21271\;18272\;13017\;22000]{\rm{Mb}}$,
$[21271\;18272\;13017\;22000\;22224]{\rm{Mb}}$, respectively. As shown in Fig.
5. (a), the average MOS values of the EC-VE algorithm and Greedy EC-VE
algorithm increase with the increasing number of EC servers. They reach to the
same maximum value when the total caching capacity of all EC servers is
sufficient. In this case, encoding packets of all video files are cached on EC
servers in the maximum encoding rates, just as the last point shows marked by
purple circle in Fig. 5. (a). The performance of the EC-VE scheme is
significantly superior to other schemes.

Besides, the average MOS values of the ECST scheme, the EC-BF scheme and the
EC-TM scheme initially rise with the increasing number of EC servers, then
remain stable. The reason is that less encoding packets are cached on EC
servers due to the limited total caching capacity of EC servers. As the number
of EC servers increases, the provided caching capacity is sufficient to cache
more encoding packets on EC servers until all encoding packets are cached on
EC servers in the fixed encoding rates. This leads to the stable average MOS
of the three schemes when the number of EC servers increase to four. It is
also interesting to find that there exist infeasible solutions for each scheme
except for the EC-VE scheme. This is because the joint optimization of video
encoding and caching strategy can wisely utilize the limited caching capacity
provided by one EC server to improve QoE and ensure security by flexibly
adjusting encoding parameters and caching strategy while other schemes cannot,
just as the first point shows marked by red circle in Fig. 5. (a).

###  VII-E Transmission Latency with Different Caching Capacity of EC Server

In Fig. 5. (b), the transmission latency versus different caching capacity of
EC server with $n=20$, $F=8$, $K=1$ is presented. To solely show the
performance of transmission latency, the fixed encoding rates of video files
in the ECST scheme, EC-BF scheme and EC-TM scheme are set as the same encoding
rate, i.e., ${{R_{\min}}}$. As shown in Fig. 5. (b), the transmission latency
of the EC-VE scheme, Greedy EC-VE scheme, ECST scheme, EC-BF scheme and EC-TM
scheme decreases with the increasing caching capacity of EC server. The
transmission latency of the Greedy EC-VE scheme, ECST scheme and EC-TM scheme
decreases to zero when the caching capacity is
${\Phi_{k}}=26880\text{Mb},\forall k\in{\cal{K}}$ because all encoding packets
can be cached on EC server at the fixed minimum encoding rates due to the
sufficient caching capacity. In general, the transmission latency of the EC-VE
scheme is lower than the ECST scheme, which is lower than other schemes. This
phenomenon strongly proves the performance advantage of the proposed EC-VE
scheme in reducing transmission latency. It can find the tradeoff between
video encoding quality and transmission latency by adjusting the cached
encoding packets sizes when caching capacity is limited, which leads to its
non-zero value at the last point in Fig. 5. (b). Besides, the ECST scheme
outperforms the Greedy EC-VE scheme. This is because the goal of the ECST
scheme is to minimize the backhaul links rate. It aims to cache as many
encoding packets as possible on EC servers with available caching capacity.
Besides, the transmission latency of the EC-TM scheme does not decrease to
zero because more caching capacity is needed to cache the encrypted video
files.

###  VII-F Minimum Caching Capacity with Different Number of Requests of Users

Figure 6: Minimum caching capacity vs. different number of total requests.

Fig. 6 shows the minimum caching capacity of the EC server versus different
number of total requests with $n=10$, $F=8$, $K=1$. Because the minimum
caching capacity is required, the fixed encoding rates of video files in the
ECST scheme, EC-BF scheme and EC-TM scheme are set as the minimum encoding
rate, i.e., ${{R_{\min}}}$. The minimum caching capacity of the five schemes
increases with the increasing number of total requests and eventually tends to
the same value when the number of total requests reaches $\psi=130$. This is
because more caching capacity is needed to cache more video encoding packets
to ensure the requirements of video encoding quality, transmission latency and
security constraints as the number of total requests increases. Furthermore,
Fig. 6 shows that the minimum caching capacity of the proposed EC-VE algorithm
is much smaller than that of the Greedy EC-VE algorithm, the ECST scheme and
the EC-TM scheme. This phenomenon shows that the proposed EC-VE algorithm
still has relatively good performance even with limited caching resources.
Meanwhile, it can spare more caching resources to achieve better video
encoding quality and low latency when satisfying the security constraints.

It is interesting to find that the gap of the minimum caching capacity between
EC-VE algorithm and the EC-BF scheme is relatively small when the number of
total requests is $\psi=70$ and $\psi=90$. This reflects the advantage of the
rate adaptive scheme EC-BF compared with other schemes. Meanwhile, the minimum
caching capacity of the EC-TM scheme is much larger than other schemes because
encrypted video files require more caching capacity under the same conditions.
The minimum caching capacity of other four schemes except EC-TM scheme finally
reaches the same value as the number of total requests increases to
$\psi=130$, because more requests mean that more video encoding packets should
be cached on the EC server for any scheme. As a result, almost all video
encoding packets are cached on the EC server at the minimum encoding rates to
satisfy the security constraints and guarantee the video encoding quality and
latency requirements when the number of total requests reaches $\psi=130$.

###  VII-G Ablation Study about Video Encoding and Edge Caching

In this subsection, the impact of video encoding module and edge caching
module on the performance of MOS, average MOS and the minimum caching capacity
to ensure secure transmission is analyzed. For comparison, in addition to our
proposed near-optimal EC-VE algorithm, the other two algorithms which are
solely based on video encoding or edge caching are considered and presented:

  * •

EC (Edge Caching): Edge caching based algorithm which solely utilizes edge
caching to improve video encoding quality and reduce latency under secure
transmission for the backhaul links.

  * •

VE (Video Encoding): Video encoding based algorithm which solely utilizes
video encoding to improve video encoding quality and reduce latency under
secure transmission for the backhaul links.

Figure 7: MOS of each video file.

Fig. 7 shows the MOS value of each video file with $F=8$, $n=18$, $K=1$ and
${\Phi_{k}}=28000\text{Mb},\forall k\in{\cal{K}}$. From Fig. 7, for each video
file, the MOS values of the EC-VE algorithm, EC algorithm and VE algorithm are
different. The average MOS values of them are 3.8172, 3.4075 and 3.5371,
respectively. Although the EC-VE algorithm outperforms the other two in the
average sense, for each video file, it is not always better. This is because
the EC-VE scheme can obtain the whole performance superiority by jointly
adjusting edge caching strategy and video encoding parameters, while the EC
scheme and VE scheme can improve MOS for certain files by only utilizing edge
caching or video encoding strategy. As shown in Fig. 7, the 1-st to 6-th video
files are more likely to be allocated more caching capacity to achieve higher
QoE with relatively low encoding rate, while the 7-th and 8-th video files are
allocated less caching capacity. This is because the QoE requirements of the
7-th and 8-th video files with high encoding rates demand more caching
capacity. Furthermore, the MOS performance of the VE scheme performs better
than that of the EC scheme. This demonstrates the advantage of video encoding
strategy with limited caching capacity.

Figure 8: (a) Average MOS vs. different caching capacity of EC server. (b)
Average MOS vs. different number of video files.

Fig. 8. (a) shows the average MOS versus different caching capacity of EC
server with $F=8$, $n=20$ and $K=1$. As shown in Fig. 8. (a), the average MOS
values of the EC-VE scheme and VE scheme rise with increasing caching
capacity, while the average MOS value of the EC scheme keeps stable when
caching capacity increases. This is because for the EC scheme, all packets are
cached on EC server with the fixed minimum encoding rates which cannot be
adjusted when the caching capacity changes, while the EC-VE scheme and VE
scheme can obtain higher QoE by encoding video files into higher encoding
rates when more caching capacity are provided. Furthermore, it is interesting
to find that the VE scheme and the EC scheme cannot achieve secure
transmission when caching capacity is very low as marked by the purple circle
in Fig. 8. (a). The MOS values of the EC-VE scheme and the VE scheme are the
same at the point marked by the black circle in Fig. 8. (a) when caching
capacity increases. This is because all encoding packets of video files are
cached on EC server when caching capacity is enough. For the VE scheme, all
video files are assumed to be cached on the EC server to ensure secure
transmission because caching strategy cannot be adjusted. The MOS superiority
of the VE scheme to the EC scheme also proves the advantage of encoding
strategy compared with caching strategy.

Fig. 8. (b) shows the average MOS versus different number of video files with
$n=10$, $K=1$ and ${\Phi_{k}}=39000\text{Mb},\forall k\in{\cal{K}}$. As marked
by the black circles in Fig. 8. (b), when the number of video files is 4 and
8, the average MOS values of the EC-VE scheme and the VE scheme decrease with
the increasing number of video files, while the average MOS of the EC scheme
remains stable. The EC-VE scheme and the VE scheme have the same performance,
which is significantly superior to that of the EC scheme. This is because the
EC-VE scheme and the VE scheme achieve the highest average MOS values with the
maximum encoding rates when the caching capacity is sufficient to cache all
encoding packets on EC server. The EC scheme shows the constant average MOS
value with all video files being encoded into the minimum encoding rates. When
the number of video files is more than 8, only the EC-VE scheme can ensure
secure transmission of all video files by caching less encoding packets of
each video file and encoding each video file into lower encoding rate under
limited caching capacity. The EC scheme and the VE scheme solely depending on
caching strategy or encoding strategy cannot find feasible solutions when the
number of video files exceeds 8.

Figure 9: Minimum caching capacity vs. different number of total requests.

Fig. 9 shows the minimum caching capacity of the EC server versus different
number of total requests with $n=10$, $F=8$, $K=1$. The minimum caching
capacity of the EC-VE scheme and the EC scheme increases with the number of
video total requests and reaches the same value at the last point. The EC-VE
scheme requires much less caching capacity to ensure security than the EC
scheme. Even if the minimum encoding rates are adopted by the EC scheme to
obtain the minimum caching capacity to ensure security, the minimum caching
capacity is still significantly more than that of the EC-VE scheme. This
further demonstrates the advantage of joint optimization of caching and
encoding strategy for EC-VE scheme. Meanwhile, the minimum caching capacity of
the VE scheme keeps constant as the number of total requests increases because
all encoding packets are cached on the EC server to ensure security. This
demands at least caching capacity of ${\Phi_{k}}=26880\text{Mb}$ with each
video file being encoded into the minimum encoding rate.

From the analysis above, we can know that the edge caching module is
responsible for caching enough packets with as small caching capacity as
possible to ensure secure transmission and sparing as large caching capacity
as possible for the video encoding module to obtain high video encoding
quality, while the video encoding module is responsible for encoding video
files into as high encoding rates as possible under secure transmission. When
the edge caching module acts alone and the encoding rates of video files
cannot be adjusted, the system performance is poor even if the caching
capacity is sufficient. Similarly, when the video encoding module acts alone
and the caching strategy cannot be adjusted, the limited caching capacity is
used to ensure security and there is no enough margin to improve video
encoding quality. Therefore, it is necessary to jointly optimize edge caching
module and video encoding module because they interact with each other and
cooperatively act on QoE improvement and security guarantee.

###  VII-H Complexity Analysis

In this subsection, the computational complexity of our proposed EC-VE
algorithm, Greedy EC-VE algorithm, the ECST scheme in [42], the EC-BF scheme
in [41] and the EC-TM scheme in [38] is analyzed.

(1) EC-VE: For our proposed near-optimal EC-VE algorithm, the computational
complexity is determined by the GlobalSearch algorithm and 0-1 branch and
bound method as shown in Algorithm 1. For the GlobalSearch algorithm, the
dimension of the optimization variable is ${\left({K+1}\right)\cdot n\cdot
F}$. Then, the computational complexity of the GlobalSearch algorithm can be
given by $O({{h_{g}}\left({\left({K+1}\right)\cdot n\cdot F}\right)})$, where
${h_{g}}\left(\cdot\right)$ is the number of operations positively related to
the dimension of the optimization variable. Finally, the computational
complexity of the EC-VE algorithm is
$O\left({{h_{g}}\left({\left({K+1}\right)\cdot n\cdot
F}\right)+{N_{n}}\cdot{N_{b}}\cdot{h_{g}}\left({\left({K+1}\right)\cdot n\cdot
F}\right)}\right)$.

(2) Greedy EC-VE: As shown in Algorithm 2, the computational complexity of our
proposed Greedy EC-VE algorithm is determined by the Algorithm 1 with a fixed
known ${\bf{S}}$ and the optimization algorithm of encoding parameters based
on the optimized caching strategy ${{\bf{\tilde{M}}}_{g}}$. For Algorithm 1
with a fixed known ${\bf{S}}$, since the dimension of optimization variable is
${K\cdot n\cdot F}$, then the computational complexity can be given by
$O({h_{g}}\left({K\cdot n\cdot F}\right))$. Finally, the computational
complexity of the Greedy EC-VE algorithm is $O\left({{h_{g}}\left({K\cdot
n\cdot F}\right)+{N_{n}}\cdot{N_{b}}\cdot{h_{g}}\left({K\cdot n\cdot
F}\right)}+N_{1}\cdot N_{2}\right)$.

(3) ECST and EC-TM: For the ECST scheme and EC-TM scheme, since they only aim
to optimize caching strategy without considering video encoding, then the
computational complexity is $O\left({{h_{g}}\left({K\cdot n\cdot
F}\right)+{N_{n}}\cdot{N_{b}}\cdot{h_{g}}\left({K\cdot n\cdot
F}\right)}\right)$.

(4) EC-BF: For the EC-BF scheme, since it aims to optimize caching strategy
and secure transmission rate without considering video encoding, then the
computational complexity is $O\left({{h_{g}}\left(({K\cdot n}+1\right)\cdot
F)+{N_{n}}\cdot{N_{b}}\cdot{h_{g}}\left(({K\cdot n}+1)\cdot F\right)}\right)$.

Based on the analysis above, compared with the Greedy EC-VE algorithm, the
increase in the dimension of the optimization variable in our proposed near-
optimal EC-VE algorithm brings higher computational complexity. It has a much
greater impact on the running time than the increase in the number of
iterations caused by optimizing the encoding parameters alone based on the
greedy method. In our simulation, the running time of the near-optimal EC-VE
algorithm is approximately ${30}$ times the running time of the Greedy EC-VE
algorithm. For the ECST in [42] and the EC-TM scheme in [38], the
computational complexity is lower than that of our Greedy EC-VE algorithm
because the video encoding is not considered. However, as mentioned above, the
increase in the number of iterations for optimizing the encoding parameters
has a trivial effect on the running time. Therefore, the difference of
computational complexity among the Greedy EC-VE algorithm, the ECST scheme and
the EC-TM scheme is very small and can be considered almost the same to some
extent. For the EC-BF scheme in [41], the computational complexity is higher
than that of Greedy EC-VE scheme, ECST scheme and EC-TM scheme due to the fact
that it aims to optimize caching strategy and secure transmission rate
simultaneously.

##  VIII Conclusion

In this paper, we proposed a QoE-driven cross-layer optimization scheme for
secure video transmission over the backhaul links in cloud-edge networks.
First, we developed a secure transmission model based on video encoding and
edge caching. By employing this model as the security constraint and
considering the interaction of video encoding parameters and edge caching
strategy, we formulated a joint optimization problem of video encoding
parameters and edge caching strategy to improve QoE. Then, a near-optimal
algorithm was designed to solve the joint optimization problem. Furthermore,
we proposed a greedy algorithm with low complexity to obtain the suboptimal
solution. Simulation results were presented to show that our proposed
algorithms can greatly improve video encoding quality and reduce transmission
latency under the condition of ensuring secure transmission of the backhaul
links compared with the existing algorithms. In addition, our proposed
algorithms were proven to be more robust for caching capacity and could ensure
secure transmission for more videos with limited caching capacity of edge
caching servers.

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|  Tantan Zhao received the B.S. degree in communication engineering from
Shanghai University, Shanghai, China, in 2014, and the M.S. degree in
information and communications engineering from Xi’an Jiaotong University,
Xi’an, China, in 2018. She is currently pursuing the Ph.D. degree with the
School of Information and Communications Engineering, Xi’an Jiaotong
University, China. Her research interests include video communication and
transmission, mobile edge computing and deep reinforcement learning.
---|---
|  Lijun He received the B.S. and Ph.D. degrees from the School of Information
and Communications Engineering, Xi’an Jiaotong University, Xi’an, China, in
2008 and 2016, respectively. She is currently a Associate Professor with the
School of Information and Communications Engineering, Xi’an Jiaotong
University. Her research interests include video communication and
transmission, video analysis, processing, and compression techniques.
---|---
|  Xinyu Huang received the B.S. degree from the Tsien Elite Class in the
Xidian University, in 2018. He is currently pursuing the M.S. degree on the
Information and Communications Engineering in the Xi’an Jiaotong University.
His research interests include edge computing, video transmission and deep
learning.
---|---
|  Fan Li (M’10) obtained his B.S. and Ph.D. degrees in information
engineering from Xi’an Jiaotong University, Xi’an, China, in 2003 and 2010,
respectively. From 2017 to 2018, he was a Visiting Scholar with the Department
of Electrical and Computer Engineering, University of California, San Diego.
He is currently a Professor with the School of Information and Communications
Engineering, Xi’an Jiaotong University. He has published more than 60
technical papers. His research interests include multimedia communication,
image/video coding and image/video quality assessment. He served as the Local
Chair for ICST Wicon 2011, and was a member of the Organizing Committee for
IET VIE 2008.
---|---