Efficient Coding for Multi-source Networks using G\'acs-K\"orner Common Information

TL;DR

This paper introduces a novel source-network coding separation method based on Gács-Körner Common Information, enabling efficient solutions for multi-source network problems without strict topological constraints.

Contribution

It proposes a new separation framework using Gács-Körner CI that depends on source structure, not network topology, and applies it to multiple multi-source network coding problems.

Findings

Characterized rate region for multi-source multicast using CI

Established duality and code constructions for broadcast with side information

Provided an efficient, tight solution for the Ahlswede-Korner problem in networks

Abstract

Consider a multi-source network coding problem with correlated sources. While the fundamental limits are known, achieving them, in general, involves a computational burden due to the complex decoding process. Efficient solutions, on the other hand, are by large based on source and network coding separation, thus imposing strict topological constraints on the networks which can be solved. In this work, we introduce a novel notion of separation of source and network coding using G\'acs-K\"orner Common Information (CI). Unlike existing notions of separation, the sufficient condition for this separation to hold depends on the source structure rather than the network topology. Using the suggested separation scheme, we tackle three important multi-source problems. The first is the multi-source multicast. We construct efficient, zero error source codes, and via properties of the CI completely characterize the resulting rate region. The second is broadcast with side information. We establish a duality between this problem and the classical problem of degraded message set broadcast, and give two code constructions and their associated regions. Finally, we consider the Ahlswede-Korner problem in a network, and give an efficient solution which is tight under the CI constraints.