The Multi-Sender Multicast Index Coding

TL;DR

This paper extends index coding theory to multiple senders with partial message knowledge, providing bounds on optimal code length and identifying cases where bounds match for the multi-sender scenario.

Contribution

It introduces a simplified pruning algorithm and an appending technique for multi-sender index coding, establishing bounds and optimality conditions using graph theory.

Findings

Lower bound derived using pruning and appending techniques.

Upper bound based on network coding principles.

Bounds match when senders have disjoint message knowledge.

Abstract

We focus on the following instance of an index coding problem, where a set of receivers are required to decode multiple messages, whilst each knows one of the messages a priori. In particular, here we consider a generalized setting where they are multiple senders, each sender only knows a subset of messages, and all senders are required to collectively transmit the index code. For a single sender, Ong and Ho (ICC, 2012) have established the optimal index codelength, where the lower bound was obtained using a pruning algorithm. In this paper, the pruning algorithm is simplified, and used in conjunction with an appending technique to give a lower bound to the multi-sender case. An upper bound is derived based on network coding. While the two bounds do not match in general, for the special case where no two senders know any message bit in common, the bounds match, giving the optimal index codelength. The results are derived based on graph theory, and are expressed in terms of strongly connected components.