On the Index Coding Problem and its Relation to Network Coding and Matroid Theory
Salim Y. El Rouayheb, Alex Sprintson, Costas N. Georghiades

TL;DR
This paper explores the index coding problem, demonstrating its deep connections to network coding and matroid theory, and shows how vector linear codes outperform scalar codes but are still insufficient for optimal solutions.
Contribution
It establishes reductions from network coding and matroid problems to index coding, revealing the limitations of linear codes and advancing theoretical understanding.
Findings
Vector linear codes outperform scalar linear codes.
Linear codes are insufficient for optimal index coding solutions.
Reductions connect index coding with network coding and matroid theory.
Abstract
The \emph{index coding} problem has recently attracted a significant attention from the research community due to its theoretical significance and applications in wireless ad-hoc networks. An instance of the index coding problem includes a sender that holds a set of information messages and a set of receivers . Each receiver needs to obtain a message and has prior \emph{side information} comprising a subset of . The sender uses a noiseless communication channel to broadcast encoding of messages in to all clients. The objective is to find an encoding scheme that minimizes the number of transmissions required to satisfy the receivers' demands with \emph{zero error}. In this paper, we analyze the relation between the index coding problem, the more general network coding problem and the problem of finding a linear representation…
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Taxonomy
TopicsCooperative Communication and Network Coding · Full-Duplex Wireless Communications · Mobile Ad Hoc Networks
