Two-Bit Message Passing Decoders for LDPC Codes Over the Binary Symmetric Channel

TL;DR

This paper introduces two-bit message passing decoders for LDPC codes over the binary symmetric channel, balancing performance and decoding speed, with thresholds derived via density evolution and error correction conditions analyzed.

Contribution

It proposes a new class of low-complexity, higher-precision message passing decoders with derived thresholds and error correction guarantees, improving upon traditional binary message passing algorithms.

Findings

Decoders with two-bit messages outperform binary message passing in error correction.

Thresholds for the proposed decoders are derived using density evolution.

Conditions for correcting up to three errors are established.

Abstract

In this paper, we consider quantized decoding of LDPC codes on the binary symmetric channel. The binary message passing algorithms, while allowing extremely fast hardware implementation, are not very attractive from the perspective of performance. More complex decoders such as the ones based on belief propagation exhibit superior performance but lead to slower decoders. The approach in this paper is to consider message passing decoders that have larger message alphabet (thereby providing performance improvement) as well as low complexity (thereby ensuring fast decoding). We propose a class of message-passing decoders whose messages are represented by two bits. The thresholds for various decoders in this class are derived using density evolution. The problem of correcting a fixed number of errors assumes significance in the error floor region. For a specific decoder, the sufficient conditions for correcting all patterns with up to three errors are derived. By comparing these conditions and thresholds to the similar ones when Gallager B decoder is used, we emphasize the advantage of decoding on a higher number of bits, even if the channel observation is still one bit.