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A Group Shuffled BP decoding for punctured Low-Density Parity-Check codes

Sangjoon Park, Sunyoung Lee, Seung‐Hoon Hwang, Sooyong Choi

Published Jan 1, 2010• 1 citation
Publisher

Abstract

A group shuffled belief propagation (GSBP) decoding for punctured low-density parity-check (LDPC) codes is proposed in the paper. The proposed GSBP decoding schedules the updating order of each bit node according to its recovery order in the standard BP decoding. This enables the proposed decoding to recover all punctured nodes in the first iteration with the minimum required number of groups. Calculation of the number of effective updates, which indicates the number of nonzero check-to-bit messages, shows that the proposed decoding can achieve faster decoding convergence than the layered BP (LBP) decoding for rate-compatible punctured LDPC (RCP-LDPC) codes. In the simulation results, the maximum SNR gain of the proposed decoding over the LBP decoding is about 0.9dB at the FER of 10-4.

DOI
10.1587/elex.7.1429

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A group shuffled belief propagation (GSBP) decoding for punctured low-density parity-check (LDPC) codes is proposed in the paper. The proposed GSBP decoding schedules the updating order of each bit node according to its recovery order in the standard BP decoding. This enables the proposed decoding to recover all punctured nodes in the first iteration with the minimum required number of groups. Calculation of the number of effective updates, which indicates the number of nonzero check-to-bit messages, shows that the proposed decoding can achieve faster decoding convergence than the layered BP (LBP) decoding for rate-compatible punctured LDPC (RCP-LDPC) codes. In the simulation results, the maximum SNR gain of the proposed decoding over the LBP decoding is about 0.9dB at the FER of 10-4.
While rate-compatible punctured low-density parity-check (RCP-LDPC) codes offer high flexibility in terms of code rate at a relatively low cost in implementation complexity, they are reported to require more decoding iterations than unpunctured LDPC codes. In this paper1we consider layered belief propagation decoding and propose efficient check node layering that significantly accelerates the decoding convergence of RCP-LDPC codes. We show that the proposed layering outperforms both random layering and conventional BP decoding. The performance improvements become more distinctive at high rates and they come at no additional implementation cost.
In this paper, we propose a scheduling method of the shuffled BP decoding algorithm for punctured LDPC codes. The number of iteration required to recover whole punctured variable nodes in the standard BP decoding algorithm is increased with the number of punctured variable nodes. However, only one number of iteration is required in the proposed shuffled BP scheduling regardless of the puncturing algorithm and the number of punctured variable nodes. Furthermore, the proposed shuffled BP scheduling can improve the reliability of the unpunctured variable nodes at the 1st iteration, while impossible in the layered BP scheduling if there are no check nodes that only unpunctured variable nodes participate. Simulation results verify that the proposed shuffled BP scheduling has comparable performance to the layered BP scheduling in spite of its smaller number of scheduling group at rate below 0.9.
To reduce the implementation complexity of a belief propagation (BP) based low-density parity-check (LDPC) decoder, shuffled BP decoding schedules, which serialize the decoding process by dividing a complete parallel message-passing iteration into a sequence of sub-iterations, have been proposed. The so-called group horizontal shuffled BP algorithm partitions the check nodes of the code graph into groups to perform group-by-group message-passing decoding. This paper proposes a new grouping technique to accelerate the message-passing rate. Performance of the proposed algorithm is analyzed by a Gaussian approximation approach. Both analysis and numerical experiments verify that the new algorithm does yield a convergence rate faster than that of existing conventional or group shuffled BP decoder with the same computing complexity constraint.
An iterative decoding algorithm of rate-compatible punctured low-density parity-check (RCP-LDPC) codes of high coding rates is developed. This algorithm performs a predetermined recovering process of punctured bits sums at the beginning of each iteration of the standard belief-propagation (BP) decoding algorithm. By propagating messages of two punctured bits sum, this algorithm can recover much more punctured bits than the standard BP decoding algorithm. It is shown that the proposed algorithm is applicable for RCP-LDPC codes of higher coding rates with little increase of decoding complexity.
A novel informed fixed scheduling (IFS) scheme for shuffled belief-propagation (BP) decoding of binary low-density parity-check (LDPC) code is introduced to improve the BP decoding convergence. The IFS finds an appropriate order of variable nodes in accordance with the number of updated neighbors in the code graph, ensuring that the maximum number of latest message updates is utilized within a single iteration. This allows the utilization of most reliable message updates in a timely manner, leading to faster error-rate convergence. Simulation results show that the proposed IFS scheme improves the convergence speed of BP decoder by up to 20% for regular LDPC codes and 45% for irregular LDPC codes, without affecting the error-rate performance, at medium-to-high signal-to-noise ratio over binary-input additive white Gaussian noise channel.