Quantized Iterative Message Passing Decoders with Low Error Floor for LDPC Codes

TL;DR

This paper introduces a novel (q+1)-bit quasi-uniform quantization method for LDPC decoders, which effectively reduces error floors caused by message quantization limitations, enhancing decoding performance with minimal added complexity.

Contribution

The paper proposes a new quantization scheme that improves message dynamic range in LDPC decoders, significantly lowering error floors compared to traditional fixed-point implementations.

Findings

The quasi-uniform quantizer reduces error floors in LDPC decoding.

Performance gains are achieved with minimal increase in decoder complexity.

The method is effective across various LDPC codes suffering from high error floors.

Abstract

The error floor phenomenon observed with LDPC codes and their graph-based, iterative, message-passing (MP) decoders is commonly attributed to the existence of error-prone substructures -- variously referred to as near codewords, trapping sets, absorbing sets, or pseudocodewords -- in a Tanner graph representation of the code. Many approaches have been proposed to lower the error floor by designing new LDPC codes with fewer such substructures or by modifying the decoding algorithm. Using a theoretical analysis of iterative MP decoding in an idealized trapping set scenario, we show that a contributor to the error floors observed in the literature may be the imprecise implementation of decoding algorithms and, in particular, the message quantization rules used. We then propose a new quantization method -- (q+1)-bit quasi-uniform quantization -- that efficiently increases the dynamic range of messages, thereby overcoming a limitation of conventional quantization schemes. Finally, we use the quasi-uniform quantizer to decode several LDPC codes that suffer from high error floors with traditional fixed-point decoder implementations. The performance simulation results provide evidence that the proposed quantization scheme can, for a wide variety of codes, significantly lower error floors with minimal increase in decoder complexity.