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International Conference on Information and Communication Technology Convergence (ICTC)

A Modified Min Sum Decoding Algorithm based on Approximation Enhancement for LDPC Codes

Nam Il Kim, Seung-Que Lee, Jin-Up Kim

Published Oct 21, 2020• 6 citations
Publisher

Abstract

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.

DOI
10.1109/ictc49870.2020.9289334

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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.
Decoding algorithms with strong practical value not only have good decoding performance, but also have the computation complexity as low as possible. For this purpose, the paper points out the modified min-sum decoding algorithm(M-MSA). On the condition of no increasing in the decoding complexity, it makes the error-correcting performance improved by adding the appropriate scaling factor based on the min-sum algorithm(MSA), and it is very suitable for hardware implementation. Simulation results show that this algorithm has good BER performance, low complexity and low hardware resource utilization, and it would be well applied in the future.
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.
In this paper, we present an improvement on the normalized min-sum (NMS) decoding algorithm for low density parity check codes. The modified NMS (M-NMS) algorithm introduces a more efficient adjustment for check node update computation. Taking the sub-minimum value among extrinsic information from the variable nodes into consideration, we make the correction factor varies with different iterations. Results show that, compared with standard min-sum (MS) and NMS decoding algorithms, the proposed method not only offers a better performance but also achieves a lower error floor in the high SNR region.
To offer commercial LDPC decoders with better performance, in this paper, multi-edge-type (MET) normalized scheme is proposed to improve the performance of traditional min-sum algorithm (MSA) and its modified versions. With respect to sum-product algorithm (SPA), we firstly analyze and find out that the degradations of convergence in different edge types are distinct in MSA theoretically. To compensate the different degradations above, proposed MET-normalized scheme is used in normalized min-sum algorithm (MET-NMSA). In addition, MET-based density evolution (MET-DE) is also presented to search optimized MET-scaling factors for MET-NMSA. To further verify the validity of MET-normalized scheme, Advanced Television Systems Committee (ATSC) 3.0 LDPC codes are used to evaluate MET-NMSA in comparison with the conventional algorithms, i.e., normalized min-sum algorithm (NMSA), offset min-sum algorithm (OMSA) and variable-scaling normalized min-sum algorithm (VS-NMSA). Extensive simulation results show that MET-NMSA for ATSC 3.0 LDPC decoders has at most 1.53dB, 0.21dB and 0.35dB gain over NMSA, OMSA and VS-NMSA respectively when frame error rate (FER) is at 10-4level over additive white Gaussian noise (AWGN) channels using QPSK modulation.
The Sum Product Algorithm (SPA) is known to offer the best performance in decoding large block length Low Density Parity Check (LDPC) codes. However, modifications in SPA to decrease the computation complexity have resulted in performance degradation. The Min Sum Algorithm (MSA) is one such variant, where the computation of the check-to-variable message is simplified to a minimum operation, instead of a hyperbolic tan calculation. Several modifications have been proposed in order to recover the performance loss of the MSA with respect to SPA. This paper proposes a modification to the MSA, based on the Wiener and Linear Minimum Mean Square Error (LMMSE) estimators for LDPC codes. The golden section search algorithm has been used to optimize the computations of the parameter estimation. Simulation results with these estimated parameters show that for low values of SNR, the modified algorithm outperforms MSA and provides performance close to that of SPA with a gain of 0.1 dB. For higher values of SNR, it outperforms MSA with a gain of 1.75 dB while providing an acceptable performance degradation with respect to SPA.