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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

A Method for Grouping Symbol Nodes of Group Shuffled BP Decoding Algorithm

Y. Sato, Gou Hosoya, Hideki Yagi, Shigeichi Hirasawa

Published Oct 1, 2008• 1 citation
Publisher

Abstract

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.

DOI
10.1093/ietfec/e91-a.10.2745

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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.
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.
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.
Implementing a belief propagation (BP) based LDPC decoder requires high degrees of parallelism using many component soft-in soft-output (SISO) decoding units to perform message passing from variable nodes to check nodes or vice versa. An obvious complexity-reduction solution is to serialize the decoding process, i.e., dividing a decoding iteration into several serial sub-iterations in which a sub-iteration performs only part of the complete parallel message-passing operation. The group horizontal shuffled BP (GHSBP) and vertical shuffled BP (GVSBP) algorithms respectively partition the check and variable nodes of the code graph into groups to perform group-by-group message-passing decoding. This paper proposes new techniques to improve three key elements of a GHSBP decoding algorithm, namely, the grouping method, the decoding schedule and the log-likelihood updating formulae. The (check nodes) grouping method and decoding schedule optimize certain design criterion. The new normalized min-sum updating formula with a self-adjustable correction (scaling) factor offers better nonlinear approximation. Numerical performance of new GHSBP algorithms that include part or all three new techniques indicate that the combination of the proposed grouping and decoding schedule yields a faster convergence rate and our modified min-sum algorithm gives performance superior to that of the conventional min-sum and normalized min-sum algorithm and is very close to that of the sum-product algorithm.
The belief propagation(BP-based)decoding algorithm can reduce the computational complexity by simplifying the information update in the check nodes and introducing the correlation among the transmitting information.In order to decrease the performance loss and the iteration numbers of the simplified BP-based decoding algorithm,the improved decoding algorithm combined the simplified BP-based decoding algorithm with group shuffle schedule was presented in this paper.The information update in the check nodes was speeded up and the information error probability from the stop set to the nodes in Tanner graph was significantly lowered in such improved algorithm.The MATLAB simulation results show that the improved algorithm can effectively enhance the decoding performance.
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.