Efficient Joint Network-Source Coding for Multiple Terminals with Side Information

TL;DR

This paper introduces a joint network-source coding scheme using matrix sparsification and LDPC syndrome decoding, enabling efficient, near-optimal transmission in multi-terminal networks with side information.

Contribution

It proposes a novel coding scheme that combines matrix sparsification with network coding, improving decoding efficiency and performance bounds in multi-terminal networks.

Findings

Achieves vanishing matrix density with comparable side information at receivers.

Provides bounds linking matrix sparsification performance to rate-distortion theory.

Demonstrates effective decoding at all terminals through simulations.

Abstract

Consider the problem of source coding in networks with multiple receiving terminals, each having access to some kind of side information. In this case, standard coding techniques are either prohibitively complex to decode, or require network-source coding separation, resulting in sub-optimal transmission rates. To alleviate this problem, we offer a joint network-source coding scheme based on matrix sparsification at the code design phase, which allows the terminals to use an efficient decoding procedure (syndrome decoding using LDPC), despite the network coding throughout the network. Via a novel relation between matrix sparsification and rate-distortion theory, we give lower and upper bounds on the best achievable sparsification performance. These bounds allow us to analyze our scheme, and, in particular, show that in the limit where all receivers have comparable side information (in terms of conditional entropy), or, equivalently, have weak side information, a vanishing density can be achieved. As a result, efficient decoding is possible at all terminals simultaneously. Simulation results motivate the use of this scheme at non-limiting rates as well.