the receiver has that message as side information.

5.  Let $\bm{\delta}_s=(\delta_s^{(1)},...,\delta_s^{(m)})$ be a vector whose elements correspond to the side information error resistance capability of each receiver.

6.  The sender transmits messages to receivers through an error-free broadcast channel.

Next, a $(\bm{\delta}_s,\mathcal{G})$-index code with side information errors is introduced. We consider an index code which can overcome arbitrary side information errors for each receiver, where each receiver does not know which side information is erroneous. Specifically, each receiver $R_i$ has a side information error resistance capability $\delta_s^{(i)}$ such that the receiver can decode the wanted messages even though less than or equal to $\delta_s^{(i)}$ symbols of side information are erroneous. Then, the $(\bm{\delta}_s,\mathcal{G})$-index code with side information errors is described as follows [@ICSIE].

Let $\bm{\delta}_s=(\delta_s^{(1)},...,\delta_s^{(m)})$ be the vector of side information error resistance capabilities. An index code with side information errors with parameters $(\bm{\delta}_s,\mathcal{G})$ over $\mathbb{F}_q$, denoted by a $(\bm{\delta}_s,\mathcal{G})$-ICSIE is a set of codewords having:

1.  An encoding function $\hat{F}: \mathbb{F}_q^n\rightarrow\mathbb{F}_q^N$

2.  A set of decoding functions $\hat{D}_1,\hat{D}_2,\ldots,\hat{D}_m$ such that $\hat{D}_i: {\mathbb{F}_q^N}\times{\mathbb{F}_q^{|{{\mathcal{X}}_i}|}}\rightarrow\mathbb{F}_q^{|f(i)|}$ satisfying $$\hat{D}_i(\hat{F}(\bold{\hat{X}}),{\bold{\hat{X}}}_{\tilde{{\mathcal{X}}}_i})=\bold{\hat{X}}_{f(i)}
    \nonumber$$ for all $i\in Z[m]$, $\bold{\hat{X}}\in\mathbb{F}_q^n$, and ${\rm wt}(\bold{\hat{X}}_{{\mathcal{X}}_i}-\bold{\hat{X}}_{\tilde{{\mathcal{X}}}_i})\leq\delta_s^{(i)}$, where $\bold{\hat{X}}_{\tilde{{\mathcal{X}}}_i}=(\hat{X}_{\tilde{1}},...,\hat{X}_{\tilde{|\mathcal{X}_i|}})$ is the erroneous side information vector of a receiver $R_i$.

A $(\bm{\delta}_s,\mathcal{G})$-ICSIE in [@ICSIE] 