System\
    with Random Topology
---

Coded caching, distributed storage, partial connectivity, multi-server caching, femtocaching.

Introduction {#sec:intro}
============

Coded caching and distributed storage have received significant attention in recent years to exploit the available memory space and processing power of individual network nodes to increase the throughput and efficiency of data availability. With proactive caching, part of the data can be pushed to nodes’ local cache memories during off-peak hours, called the *placement phase*, to reduce the burden on the network during peak traffic periods, called the *delivery phase* [@maddah] - [@comb1]. A different type of coded caching also improves the delivery performance in the so-called “femtocaching” scenario [@femtocaching], where multiple cache-equipped small-cell base stations (SBSs) collaboratively deliver contents to users. Coding for distributed storage systems has been extensively studied in the literature (see, for example, [@dimakis_networkcodes]), and in the femtocaching scenario, ideal maximum distance separable (MDS) codes allow users to recover contents by collecting parity bits from only a subset of SBSs they connect to [@femtocaching].

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      ![Examples of different network topologies for $P=3$ and $K=4$ with $\rho=2$.[]{data-label="fig:f1"}](fig2b.PNG "fig:"){width="22.00000%"} \[fig:f11\]
                                                            $(a)$ $\rho=2$, $q_1=2, q_2=4, q_3=2$.
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   ![Examples of different network topologies for $P=3$ and $K=4$ with $\rho=2$.[]{data-label="fig:f1"}](fig2c_2.PNG "fig:"){width="24.00000%"} \[fig:f12\]
              