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A modified Offset Min-Sum decoding algorithm for LDPC codes

Meng Xu, Jianhui Wu, Meng Zhang

Published Jul 1, 2010• 29 citations
Publisher

Abstract

In this paper a modified Offset Min-Sum decoding algorithm for Low-Density Parity Check Codes is presented. In this modified algorithm, the offset factor in the original Offset Min-Sum algorithm is adjusted iteratively with the assistance of the check-node computation outputs of the Normalized Min-Sum algorithm. As a result, the offset factor in our modified algorithm can be calculated adaptively and more efficiently according to the previous decoding procedure, which can minimize the decoding degradation compared with the Belief Propagation decoding algorithm. The simulation results show that, compared with the original Offset Min-Sum decoding algorithm, our modified algorithm can achieve noticeable performance improvement with minor extra hardware complexity. For example, when BER is 10−5, our algorithm can achieve 0.1dB and 0.2dB decoding gain over Offset Min-Sum algorithm for regular and irregular LDPC codes respectively.

DOI
10.1109/iccsit.2010.5564884

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In this paper a modified Offset Min-Sum decoding algorithm for Low-Density Parity Check Codes is presented. In this modified algorithm, the offset factor in the original Offset Min-Sum algorithm is adjusted iteratively with the assistance of the check-node computation outputs of the Normalized Min-Sum algorithm. As a result, the offset factor in our modified algorithm can be calculated adaptively and more efficiently according to the previous decoding procedure, which can minimize the decoding degradation compared with the Belief Propagation decoding algorithm. The simulation results show that, compared with the original Offset Min-Sum decoding algorithm, our modified algorithm can achieve noticeable performance improvement with minor extra hardware complexity. For example, when BER is 10−5, our algorithm can achieve 0.1dB and 0.2dB decoding gain over Offset Min-Sum algorithm for regular and irregular LDPC codes respectively.
A modified Min-Sum algorithm for low-density parity check codes is proposed in this paper. The inaccurate check node messages of the Min-Sum algorithm compared to the belief propagation (BP) algorithm are compensated by modified variable node messages, which is different from the normalized Min-Sum algorithm. The modified factor is obtained before decoding program and only one extra multiplication is needed in one cycle. So the increased complexity is fairly low. The simulation results show that the bit error rate (BER) and average number of iteration of the modified Min-Sum algorithm are very close to the BP algorithm, the modified algorithm can improve the BER performance compared to the Min-Sum algorithm while added complexity slightly.
In this paper, a modified min-sum decoding algorithm based on classified correction is proposed for low density parity check (LDPC) codes. Different from the single correction in the normalized belief propagation (BP)-based and offset BP-based algorithms [4], the proposed algorithm utilizes two corrections for both minimum and sub-minimum magnitudes of input messages in check nodes. These two correction factors can be obtained by analyzing the offset of updated messages in check nodes between the BP and the min-sum algorithms associated with check node degree. Simulation results show that the proposed algorithm can achieve performance very close to that of the BP algorithm. Furthermore, the FPGA implementation of this algorithm can reach a throughput of 200 Mbps at BER=10-6with lower complexity and fewer resources than the BP algorithm.
Offset Min-Sum Algorithm (OMSA) and Normalized Min-Sum Algorithm (NMSA) are widely used in commercial LDPC decoders due to low complexity and reasonable performance. In this paper we proposes an Adaptive Layered Offset min- sum algorithm for the decoding of LDPC codes, which utilizes an adaptive offset factor to improve the accuracy of the soft information transferred during the iterative decoding process, and it provides good performance accordingly. The performed simulations showed that the layered offset min-sum decoding for LDPC codes can provide significant improvement compared to existing MS based algorithm, OMSA and NMSA.
A check node degree-based modified min-sum algorithm which classifies the codes was developed to reduce the complexity and improve the performance of decoding algorithm for low-density parity-check(LDPC) codes.The algorithm corrects both the minimum and sub-minimum absolute values of incoming messages in the check nodes.Two correction factors are obtained by calculating the offset between the belief propagation(BP) algorithm and the min-sum algorithm based on the check node degree.Simulations show that the algorithm achieves better performance than the BP algorithm at high signal noise ratio.The algorithm is also less complex than the BP algorithm and provides a good tradeoff between performance and complexity for any check node degree distribution in the LDPC codes.
In this paper, a modified normalized Min-Sum algorithm (MNMSA) is proposed for decoding irregular Low Density Parity Check Codes (LDPC) with non-uniform degree distribution. The proposed algorithm provides an efficient decoding scheme to enhance the error performance of an irregular LDPC code without increasing the hardware complexity. An efficient 6- bit quantization scheme is utilized in the proposed algorithm with optimally combined normalization and down scaling factors to resolve the magnitude overestimation issue which occurs during iterative message passing process between the nodes. The simulation results demonstrate that the proposed algorithm achieves good decoding performance in terms of Frame Error Rate (FER) and Bit Error Rate (BER) without the requirement of complex arithmetic calculations. Compared to other min- sum based decoding algorithms the decoding process of the proposed MNMSA requires only fewer decoding iterations over wide range of signal- to- noise ratio (SNR) to achieve comparable decoding performance to that of Belief Propagation (BP) algorithm without increasing the hardware complexity.