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IEEE Communications Letters

A Grouping Based on Local Girths for the Group Shuffled Belief Propagation Decoding

Akiko Manada, Kyohei Yoshida, Hiroyoshi Morita, Ryuichi Tatasukawa

Published Sep 20, 2016• 5 citations
Publisher

Abstract

Low-density parity-check codes have been known to exhibit good error correcting performance by using with the belief propagation (BP) decoding. The group shuffled BP decoding, which is a modification of the BP decoding, can exhibit a better performance than BP decoding by suitably grouping variable nodes in a Tanner graph. In this letter, we propose a new grouping of variable nodes based on local girths and evaluate its performance.

DOI
10.1109/lcomm.2016.2598571

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Low-density parity-check codes have been known to exhibit good error correcting performance by using with the belief propagation (BP) decoding. The group shuffled BP decoding, which is a modification of the BP decoding, can exhibit a better performance than BP decoding by suitably grouping variable nodes in a Tanner graph. In this letter, we propose a new grouping of variable nodes based on local girths and evaluate its performance.
In this paper, we propose a method for enhancing performance of a sequential version of the belief-propagation (BP) decoding algorithm, the group shuffled BP decoding algorithm for low-density parity-check (LDPC) codes. An improved BP decoding algorithm, called the shuffled BP decoding algorithm, decodes each symbol node in serial at each iteration. To reduce the decoding delay of the shuffled BP decoding algorithm, the group shuffled BP decoding algorithm divides all symbol nodes into several groups. In contrast to the original group shuffled BP, which automatically generates groups according to symbol positions, in this paper we propose a method for grouping symbol nodes which generates groups according to the structure of a Tanner graph of the codes. The proposed method can accelerate the convergence of the group shuffled BP algorithm and obtain a lower error rate in a small number of iterations. We show by simulation results that the decoding performance of the proposed method is improved compared with those of the shuffled BP decoding algorithm and the group shuffled BP decoding algorithm.
In this paper, we propose a shuffled version of the belief propagation (BP) algorithm for the decoding of low-density parity-check (LDPC) codes. We show that when the Tanner graph of the code is acyclic and connected, the proposed scheme is optimal in the sense of MAP decoding and converges faster (or at least no slower) than the standard BP algorithm. Interestingly, this new version keeps the computational advantages of the forward-backward implementations of BP decoding. Both serial and parallel implementations are considered. We show by simulation that the new schedule offers better performance/complexity trade-offs.
Shuffled decoding is known to provide efficient and high-throughput implementation of LDPC decoders. In this paper, a new grouping technique of variable nodes to accelerate the message-passing rate is presented. In this algorithm, unlike other group-shuffled decoding methods, we consider for the first sub-group a set of variable nodes that has a low value of the intrinsic information, where the variable nodes of the code graph are divided into sub-groups called layers to perform group-by-group message-passing decoding and each iteration is broken into multiple sub-iterations. This paper proposes a simplification of the Variable Node group-shuffled Belief Propagation (Optimized VN group-shuffled BP) to lower the complexity of the check node update rule. Simulation results, verify that the Optimized VN group-shuffled BP does yield a faster convergence rate than both Belief Propagation (BP) and Check Node group-shuffled Belief Propagation (CN group-shuffled BP) decoder.
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.
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.