Code Design for the Noisy Slepian-Wolf Problem

TL;DR

This paper develops LDGM and LDPC code ensembles that achieve near-optimal performance in noisy Slepian-Wolf problems over symmetric channels without transmitter channel knowledge, using density evolution and staggered structures.

Contribution

It introduces a provable capacity-achieving LDGM sequence and a staggered LDPC code framework for the noisy Slepian-Wolf problem with unknown channel parameters.

Findings

LDGM ensembles achieve capacity for erasure Slepian-Wolf with symmetric channels.

Staggered LDPC codes improve performance over a wide range of channel conditions.

Density evolution analysis guides the design of robust codes.

Abstract

We consider a noisy Slepian-Wolf problem where two correlated sources are separately encoded (using codes of fixed rate) and transmitted over two independent binary memoryless symmetric channels. The capacity of each channel is characterized by a single parameter which is not known at the transmitter. The goal is to design systems that retain near-optimal performance without channel knowledge at the transmitter. It was conjectured that it may be hard to design codes that perform well for symmetric channel conditions. In this work, we present a provable capacity-achieving sequence of LDGM ensembles for the erasure Slepian-Wolf problem with symmetric channel conditions. We also introduce a staggered structure which enables codes optimized for single user channels to perform well for symmetric channel conditions. We provide a generic framework for analyzing the performance of joint iterative decoding, using density evolution. Using differential evolution, we design punctured systematic LDPC codes to maximize the region of achievable channel conditions. The resulting codes are then staggered to further increase the region of achievable parameters. The main contribution of this paper is to demonstrate that properly designed irregular LDPC codes can perform well simultaneously over a wide range of channel parameters.