Graph-Theoretic Approaches to Two-Sender Index Coding

TL;DR

This paper investigates two-sender index coding, using graph theory to extend single-sender schemes and analyze the minimal transmissions needed for cooperative message broadcasting.

Contribution

It introduces a graph-theoretic framework for two-sender unicast index coding and extends existing single-sender schemes to this new setting.

Findings

TSUIC is equivalent to SSUIC in certain cases

Extended cycle-cover, clique-cover, and local-chromatic schemes to TSUIC

Provided insights into minimizing transmissions in cooperative broadcast scenarios

Abstract

Consider a communication scenario over a noiseless channel where a sender is required to broadcast messages to multiple receivers, each having side information about some messages. In this scenario, the sender can leverage the receivers' side information during the encoding of messages in order to reduce the required transmissions. This type of encoding is called index coding. In this paper, we study index coding with two cooperative senders, each with some subset of messages, and multiple receivers, each requesting one unique message. The index coding in this setup is called two-sender unicast index coding (TSUIC). The main aim of TSUIC is to minimize the total number of transmissions required by the two senders. Based on graph-theoretic approaches, we prove that TSUIC is equivalent to single-sender unicast index coding (SSUIC) for some special cases. Moreover, we extend the existing schemes for SSUIC, viz., the cycle-cover scheme, the clique-cover scheme, and the local-chromatic scheme to the corresponding schemes for TSUIC.