Index Coding - An Interference Alignment Perspective

TL;DR

This paper explores index coding through interference alignment, establishing equivalences and conditions for optimal rates, and providing capacity solutions for symmetric problems inspired by wireless network characteristics.

Contribution

It introduces an equivalence between unicast and groupcast index coding, and derives conditions for achievable rates using interference alignment, advancing the understanding of index coding capacity.

Findings

Equivalence between multiple unicast and groupcast index coding.

Necessary and sufficient conditions for rate half per message.

Capacity optimal solutions for symmetric index coding problems.

Abstract

The index coding problem is studied from an interference alignment perspective, providing new results as well as new insights into, and generalizations of, previously known results. An equivalence is established between multiple unicast index coding where each message is desired by exactly one receiver, and multiple groupcast index coding where a message can be desired by multiple receivers, which settles the heretofore open question of insufficiency of linear codes for the multiple unicast index coding problem by equivalence with multiple groupcast settings where this question has previously been answered. Necessary and sufficient conditions for the achievability of rate half per message are shown to be a natural consequence of interference alignment constraints, and generalizations to feasibility of rate $\frac{1}{L+1}$ per message when each destination desires at least $L$ messages, are similarly obtained. Finally, capacity optimal solutions are presented to a series of symmetric index coding problems inspired by the local connectivity and local interference characteristics of wireless networks. The solutions are based on vector linear coding.