# Index coding with erroneous side information

## TL;DR

This paper introduces a new index coding problem considering erroneous side information, proposing encoding/decoding methods, bounds on code length, and generalizations to handle both side information and channel errors.

## Contribution

It presents the first study of index coding with erroneous side information, including syndrome decoding-based procedures, bounds, and a novel graph structure called δ_s-cycle.

## Key findings

- Proposed encoding and decoding procedures for ICSIE.
- Derived bounds on the optimal codelength.
- Generalized to handle both side information and channel errors.

## Abstract

In this paper, new index coding problems are studied, where each receiver has erroneous side information. Although side information is a crucial part of index coding, the existence of erroneous side information has not yet been considered. We study an index code with receivers that have erroneous side information symbols in the error-free broadcast channel, which is called an index code with side information errors (ICSIE). The encoding and decoding procedures of the ICSIE are proposed, based on the syndrome decoding. Then, we derive the bounds on the optimal codelength of the proposed index code with erroneous side information. Furthermore, we introduce a special graph for the proposed index coding problem, called a $\delta_s$-cycle whose properties are similar to those of the cycle in the conventional index coding problem. Properties of the ICSIE are also discussed in the $\delta_s$-cycle and clique. Finally, the proposed ICSIE is generalized to an index code for the scenario having both additive channel errors and side information errors, called a generalized error correcting index code (GECIC).