# Equivalences Between Network Codes With Link Errors and Index Codes With Side Information Errors

## TL;DR

This paper establishes new equivalence relationships between network codes with link errors and index codes with side information errors, enabling the transfer of properties and insights between these two coding frameworks.

## Contribution

It introduces methods to convert between network codes with link errors and index codes with side information errors, revealing their fundamental equivalences.

## Key findings

- Derived equivalent index coding instances from network coding instances.
- Established conditions for converting ICSIE to NCLE and vice versa.
- Properties of NCLEs can be inferred from properties of equivalent ICSIEs.

## Abstract

In this paper, new equivalence relationships between a network code with link errors (NCLE) and an index code with side information errors (ICSIE) are studied. First, for a given network coding instance, the equivalent index coding instance is derived, where an NCLE is converted to the corresponding ICSIE and vice versa. Next, for a given index coding instance, the equivalent network coding instance is also derived, where an ICSIE is converted to the corresponding NCLE and vice versa if a pair of encoding functions of an original link and the duplicated link are functionally related in the network code. Finally, several properties of an NCLE are derived from those of the equivalent ICSIE using the fact that the NCLE and the ICSIE are equivalent.