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Science Technology and Engineering

Improved Min-sum Decoding Algorithm for LDPC Codes

MU Jian-jun

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

Compared with the BP decoding algorithm,the min-sum decoding algorithm has higher error floor for LDPC codes over the binary symmetric channel(BSC).In order to solve this problem,a modified algorithm is presented.The proposed algorithm can reduce memory overhead and accelerate the convergence of decoding algorithm by using the thought of multi-level quantification and considering the knowledge both extra messages for each node and received values from the channel,respectively.Simulation results show that the improved min-sum algorithm with three or four levels approach and even surpass floating-point BP decoding algorithm in frame error rate(FER) performance over the BSC.

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Compared with the BP decoding algorithm,the min-sum decoding algorithm has higher error floor for LDPC codes over the binary symmetric channel(BSC).In order to solve this problem,a modified algorithm is presented.The proposed algorithm can reduce memory overhead and accelerate the convergence of decoding algorithm by using the thought of multi-level quantification and considering the knowledge both extra messages for each node and received values from the channel,respectively.Simulation results show that the improved min-sum algorithm with three or four levels approach and even surpass floating-point BP decoding algorithm in frame error rate(FER) performance over the BSC.
Min-sum algorithm(MSA) and its modification are used in LDPC decoder implementations because of its error performance and low computation complexity. In this paper a modified min-sum LDPC decoding algorithm through approximation enhancement using the smallest three minimum values is presented. The proposed algorithm improves error performance and reduces decoder iterations. From the simulation results for 5G NR LDPC codes, we show that the proposed algorithm can achieve about 1.6dB improvement of FER compared to the min-sum decoding algorithm and provide about 10% reduction of the average iteration numbers compare to NMSA with optimum normalization factor.
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.
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 letter, an enhanced verification-based decoding algorithm (EVA) for packet level low-density parity-check (LDPC) codes is proposed. Compared with the verification algorithm (VA) in the literature, the proposed algorithm reduces the likelihood of false verification by enhancing the verification condition to achieve a better decoding performance. For example, simulation results in this letter show that EVA reduces frame error rate (FER) by two orders when comparing the VA over binary symmetric channel (BSC), while the increase of the computational load is less than 90%.
In order to make up for the performance defects of Min-sum decoding algorithm relative to LLR BP decoding algorithm and reduce implementation complexity of LLR-BP algorithm,a modified Min-sum decoding algorithm is proposed.When the check nodes process the message,parameters of the proposed algorithm are confirmed according to minimum mean square error rule,and the normalized BP-based decoding algorithm and the offset BP-based decoding algorithm are integrated effectively.At the same time,we introduce the correction factor and the offset factor into this algorithm reasonably.The simulation results show that decoding performance of modified Min-sum decoding algorithm is more effective than that of Min-sum decoding algorithm,normalized BP-based decoding algorithm and offset BP-based decoding algorithm under the same condition of bit error rate,and it approaches to the performance of LLR-BP decoding algorithm.
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.