Parallel vs. Sequential Belief Propagation Decoding of LDPC Codes over GF(q) and Markov Sources

TL;DR

This paper introduces a sequential belief propagation decoding scheme for LDPC codes over GF(q) and Markov sources, demonstrating it converges twice as fast as the standard parallel scheme without performance loss.

Contribution

The paper proposes and experimentally validates a sequential updating scheme for belief propagation decoding that significantly improves convergence speed over the parallel scheme.

Findings

SUS halves the number of iterations needed for convergence compared to PUS.

The convergence speed-up factor is consistent across different field sizes and source/channel correlations.

Error correction performance remains unaffected by the switch from PUS to SUS.

Abstract

A sequential updating scheme (SUS) for belief propagation (BP) decoding of LDPC codes over Galois fields, $GF(q)$, and correlated Markov sources is proposed, and compared with the standard parallel updating scheme (PUS). A thorough experimental study of various transmission settings indicates that the convergence rate, in iterations, of the BP algorithm (and subsequently its complexity) for the SUS is about one half of that for the PUS, independent of the finite field size $q$. Moreover, this 1/2 factor appears regardless of the correlations of the source and the channel's noise model, while the error correction performance remains unchanged. These results may imply on the 'universality' of the one half convergence speed-up of SUS decoding.