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Communications, Internet, and Information Technology

Nonlinear Dynamics of the Message Passing Decoder of LDPC Codes.

G.M. Maggio, Frédéric Lehmann, Ljupčo Kocarev, Žarko Tasev

Published Jan 1, 2002• 0 citations
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Efficient hardware implementation of low-density parity-check (LDPC) codes is of great interest since LDPC codes are being considered for a wide range of applications. Recently, overlapped message passing (OMP) decoding has been proposed to improve the throughput and hardware utilization efficiency (HUE) of decoder architectures for LDPC codes. In this paper, we first study the scheduling for the OMP decoding of LDPC codes, and show that maximizing the throughput gain amounts to minimizing the intra- and inter-iteration waiting times. We then focus on the OMP decoding of quasi-cyclic (QC) LDPC codes. We propose a partly parallel OMP decoder architecture and implement it using FPGA. For any QC LDPC code, our OMP decoder achieves the maximum throughput gain and HUE due to overlapping, hence has higher throughput and HUE than previously proposed OMP decoders while maintaining the same hardware requirements. We also show that the maximum throughput gain and HUE achieved by our OMP decoder are ultimately determined by the given code. Thus, we propose a coset-based construction method, which results in QC LDPC codes that allow our optimal OMP decoder to achieve higher throughput and HUE.
In this paper we introduce a novel one-dimensional model of the message passing decoding algorithm of low-density parity-check (LDPC) codes, based on Gaussian densities. The model consists of a closed-form 1-D map whose iterates directly represent the error probability. This map allows a qualitative analysis of the nonlinear dynamics of the decoding algorithm. Moreover, it is shown that our approach leads to the correct stability condition and that the corresponding threshold values are in good agreement with density evolution.