Error Correction for Index Coding With Coded Side Information
Eimear Byrne, Marco Calderini

TL;DR
This paper studies the problem of designing optimal index codes with coded side information and error correction, providing bounds, characterizations, and decoding algorithms for these complex scenarios.
Contribution
It introduces a generalized min-rank characterization for optimal linear index codes with coded side information and error correction, advancing the theoretical understanding of these problems.
Findings
Characterized the optimal length of scalar and vector linear index codes with coded side information.
Provided bounds on the length of error-correcting index codes for noisy channels.
Developed decoding algorithms for both Hamming and rank-metric errors.
Abstract
Index coding is a source coding problem in which a broadcaster seeks to meet the different demands of several users, each of whom is assumed to have some prior information on the data held by the sender. If the sender knows its clients' requests and their side-information sets, then the number of packet transmissions required to satisfy all users' demands can be greatly reduced if the data is encoded before sending. The collection of side-information indices as well as the indices of the requested data is described as an instance of the index coding with side-information (ICSI) problem. The encoding function is called the index code of the instance, and the number of transmissions employed by the code is referred to as its length. The main ICSI problem is to determine the optimal length of an index code for and instance. As this number is hard to compute, bounds approximating it are…
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