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IET Communications

Improved min‐sum algorithm based on density evolution for low‐density parity check codes

Xiumin Wang, Weilin Cao, Jun Li, Liang Shan, Haiyan Cao, Jinsong Li, Fanglei Qian

Published Apr 28, 2017• 9 citations
Publisher

Abstract

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.

DOI
10.1049/iet-com.2017.0014

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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.
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.
The min‐sum algorithm (MSA) for decoding Low‐Density Parity‐Check (LDPC) code is an approximation algorithm that can greatly reduce the computational complexity of the belief propagation algorithm (BPA). To reduce the error between MSA and BPA, an improved MSA such as normalized min‐sum algorithm (NMSA) that uses the normalization factor when updating the check node is used in many LDPC decoders. When obtaining an optimal normalization factor, density evolution (DE) is usually used. However, not only does the DE method require a large number of calculations, it may not be optimal for obtaining a normalization factor due to the theoretical assumptions that need to be satisfied. This paper proposes a new method obtaining a normalization factor for NMSA. We first examine the relationship between the minimum value of variable node messages’ magnitudes and the magnitudes of check node outputs of BPA using the check node message distribution (CMD) chart. And then, we find a normalization factor that minimizes the error between the magnitudes of check node output of NMSA and BPA. We use the least square method (LSM) to minimize the error. Simulation on ATSC 3.0 LDPC codes demonstrates that the normalization factor obtained by this proposed method shows better decoding performance than the normalization factor obtained by DE.
In this study, the authors propose an improved version of the min-sum algorithm for low-density parity check code decoding, which the authors call ‘adaptive normalised BP-based’ algorithm. Their decoder provides a compromise solution between belief propagation and the min-sum algorithms by adding an exponent offset to each variable node's intrinsic information in the check node update equation. The extrinsic information from the min-sum decoder is then adjusted by applying a negative power of the two scale factor, which can be easily implemented by right shifting the min-sum extrinsic information. The difference between their approach and other adaptive normalised min-sum decoders is that the authors select the normalisation scale factor using a clear analytical approach based on the underlying principles. The simulation results show that the proposed decoder outperforms the min-sum decoder and performs very close to the BP decoder with lower complexity.
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 improve performance and reduce computation complexity of the low-density parity-check (LDPC) codes, a min-sum based differential decoding algorithm is proposed. The main principle is that the messages passing in the bipartite graph of the codes are the probability differences and the updates of the check nodes adopt min sum algorithm. Simulation results show that the proposed algorithm can achieve about 0.4dB performance gain over the UMP BP-Based decoding algorithm at bit error rate (BER) of under an additive white Gaussian noise (AWGN) channel. And it can obtain good performance very close to that of the BP decoding algorithm with much lower complexity.