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AEU - International Journal of Electronics and Communications

A modified Min Sum decoding algorithm based on LMMSE for LDPC codes

Zijing Wu, Kaixiong Su, Liting Guo

Published May 10, 2014• 10 citations
Publisher
DOI
10.1016/j.aeue.2014.04.024

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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.
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 study, the authors present an improved min‐sum (MS) algorithm based on density evolution (DE) called the DE MS algorithm for low‐density parity check codes. First, they use DE theory to calculate the probability density function of the check‐to‐variable message of the belief propagation (BP) algorithm and the MS/normalised MS (NMS) algorithm and furthermore to calculate the normalised factor α . Then, α is modified further by using the weighted average. Finally, in order to ensure the decoding performance and reduce the hardware complexity, the same α is used for different signal‐to‐noise ratios. The simulation results show that a gain of about 0.2 dB can be achieved in comparison with the classical NMS algorithm. In addition, this algorithm can obtain the same decoding performance compared with the Linear Minimum Mean Square Error (LMMSE) MS algorithm whose decoding performance is very close to that of the BP algorithm, and it also saves around 24.57% of logic elements and 34.33% of memory bits compared with the LMMSE MS algorithm at the same time.