Can Iterative Decoding for Erasure Correlated Sources be Universal?

TL;DR

This paper investigates the universality of iterative decoding schemes for joint source-channel coding of correlated erasure sources over different channels, analyzing the performance of LT and LDPC codes.

Contribution

It demonstrates that optimized LT codes can reach the symmetric capacity point but are not universal for all capacity region points, highlighting limitations of iterative decoding.

Findings

LT codes achieve the extremal symmetric point of the capacity region

LT codes are not universal under iterative decoding for all capacity points

Density evolution characterizes the sub-universality of LT codes

Abstract

In this paper, we consider a few iterative decoding schemes for the joint source-channel coding of correlated sources. Specifically, we consider the joint source-channel coding of two erasure correlated sources with transmission over different erasure channels. Our main interest is in determining whether or not various code ensembles can achieve the capacity region universally over varying channel conditions. We consider two ensembles in the class of low-density generator-matrix (LDGM) codes known as Luby-Transform (LT) codes and one ensemble of low-density parity-check (LDPC) codes. We analyze them using density evolution and show that optimized LT codes can achieve the extremal symmetric point of the capacity region. We also show that LT codes are not universal under iterative decoding for this problem because they cannot simultaneously achieve the extremal symmetric point and a corner point of the capacity region. The sub-universality of iterative decoding is characterized by studying the density evolution for LT codes.