Analysis and Design of Binary Message-Passing Decoders

TL;DR

This paper analyzes binary message-passing decoders for LDPC codes using EXIT charts, demonstrating performance gains with optimized codes and establishing conditions for cycle-free decoding.

Contribution

It introduces a method to optimize binary message-passing decoders by adapting EXIT functions and derives conditions for cycle-free subgraphs in LDPC decoding.

Findings

Increasing output alphabet improves SNR performance by over 1 dB.

Errors on certain cycles cannot be corrected, affecting decoder design.

A necessary and sufficient condition for cycle-free subgraphs is established.

Abstract

Binary message-passing decoders for low-density parity-check (LDPC) codes are studied by using extrinsic information transfer (EXIT) charts. The channel delivers hard or soft decisions and the variable node decoder performs all computations in the L-value domain. A hard decision channel results in the well-know Gallager B algorithm, and increasing the output alphabet from hard decisions to two bits yields a gain of more than 1.0 dB in the required signal to noise ratio when using optimized codes. The code optimization requires adapting the mixing property of EXIT functions to the case of binary message-passing decoders. Finally, it is shown that errors on cycles consisting only of degree two and three variable nodes cannot be corrected and a necessary and sufficient condition for the existence of a cycle-free subgraph is derived.