they have identical erroneous incoming symbols. The above encoding functions of links are local functions. However, the global function $\bar{F}_e$ is defined as $\bar{F}_e(\bold{\tilde{X}}_S)=F_e(\bold{\tilde{X}}_{{\rm In}(e)})$.

Index Codes With Side Information Errors
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We introduce index codes with side information errors as in [@ICSIE]. First, an index coding instance is described as follows:

1.  There are one sender which has $n$ information messages as $\bold{\hat{X}}=(\hat{X}_1,\ldots,\hat{X}_n)\in\mathbb{F}_q^n$ and $m$ receivers (or users) $R_1,R_2,\ldots,R_m$, having sub-vectors of $\bold{\hat{X}}$ as side information.

2.  Let ${{\mathcal{X}}_i}$ be the set of side information indices of a receiver $R_i$ for $i\in Z[m]$.

3.  Each receiver $R_i$ wants to receive some elements in $\bold{\hat{X}}$, referred to as the wanted messages denoted by $\bold{\hat{X}}_{f(i)}$, where $f(i)$ represents the set of indices of the wanted messages of $R_i$ and $f(i)\cap{{\mathcal{X}}_i}=\phi$.

4.  A side information graph $\mathcal{G}$ shows the wanted messages and side information of all receivers and the sender knows $\mathcal{G}$. A side information graph is a bipartite graph which consists of message nodes and receiver nodes. A directed edge from a message node to a receiver node means that the receiver wants to receive that message. Conversely, a directed edge from a receiver node to a message node means that 