$(X_{i_1},X_{i_2},\ldots,X_{i_{|D|}})$ of a vector $\bold{X}=(X_1,X_2,\ldots,X_n)\in \mathbb{F}_q^n$ for a subset $D=\{i_1,i_2,\ldots,i_{|D|}\}\subseteq Z[n]$, where $i_1<i_2<\ldots<i_{|D|}$.

Network Codes With Link Errors
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In this paper, in order to provide an equivalence between an NCLE and an ICSIE for any given index coding instance, a generalized network coding scenario is considered, where each internal node can resolve their erroneous incoming symbols.

For this scenario, if we know the probability distribution of the link errors, the throughput gain can be improved by assigning suitable error resistance capabilities to the internal nodes in a network structure. That is, large error resistance capabilities of internal nodes for the vulnerable links can improve throughput gain of an entire network because error propagation may be moderated. In this perspective, we introduce a new network code which deals with erroneous data on links.

First, we introduce a network coding instance with a network structure ${\mathbb{G}}=(V,E,\mathcal{F})$, where $V$ and $E$ denote the sets of nodes and edges in $\mathbb{G}$, respectively and a vector of the error resistance capabilities $\bm{\delta}$ described by a directed acyclic graph and a function of terminals $\mathcal{F}$ as follows:

1.  $\bar{S}\subseteq V$ denotes a set of source nodes in ${\mathbb{G}}$, where source nodes do not have incoming 