are the error resistance capabilities and the existence of the receiver $\hat{t}_{\rm all}$. In what follows, the relationship between two coding instances of a $(\bm{\delta},\mathbb{G})$-NCLE and the corresponding $(\bm{\delta}_s,\mathcal{G})$-ICSIE is given as follows:

1.  A sender of a $(\bm{\delta}_s,\mathcal{G})$-ICSIE has a message $\bold{\hat{X}}=(\bold{\hat{X}}_S, \bold{\hat{X}}_E)$ and there are $|E|+|T|$ receivers, each of which is a corresponding receiver $R_e$ of a link or $R_t$ of a terminal in a given network coding instance.

2.  For $e\in E$, $R_e$ of the $(\bm{\delta}_s,\mathcal{G})$-ICSIE can be described as $\mathcal{X}_e={\rm In}(e)$, $f(e)=\{e\}$, and $\delta_s^{(e)}=\delta_e$.

3.  For $t\in T$, $R_t$ of the $(\bm{\delta}_s,\mathcal{G})$-ICSIE can be described as $\mathcal{X}_t={\rm In}(t)$, $f(t)=\mathcal{F}(t)$, and $\delta_s^{(t)}=\delta_t$.

4.  The codelength of the $(\bm{\delta}_s,\mathcal{G})$-ICSIE is the number of links in a $(\bm{\delta},\mathbb{G})$-NCLE.

This relationship is derived from a given network coding instance. Fig. \[fig:network example\] shows an example of a network coding instance and the corresponding index coding instance. Before showing validity of this model, some restrictions for the corresponding index coding instance should be satisfied as shown in the following proposition.

The corresponding index coding instance of a given network coding instance should satisfy the followings:

1.  In the corresponding side information graph $\mathcal{G}$, there is no cycle in a subgraph which 