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Wireless Communications and Mobile Computing

An Alternative Approach Obtaining a Normalization Factor in Normalized Min‐Sum Algorithm for Low‐Density Parity‐Check Code

In-Woo Yun, Hee-ran Lee, Joon Tae Kim

Published Jan 1, 2018• 7 citations
Publisher

Abstract

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.

DOI
10.1155/2018/1398191

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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 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 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.
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.
This paper proposes a new technique to improve bit error performance of the min-sum decoding algorithm for low density parity check codes. The proposed technique is based on two way normalization of min-sum LDPC decoding algorithm. The variable message is modified by two normalization factors to achieve the optimum approximation for the magnitude overestimation at the check node processing. This new method does not need exhaustive search for the optimum normalization factor when there is a change in code length and code rate. The performance has been evaluated for medium and short length codes using a small number of iterations. The results show improved performance of the proposed method, which makes it attractive for many practical applications.
The belief propagation (BP) algorithm for low density parity check (LDPC) codes has proven to have excellent performance and is close to the Shannon limit. However, the high computational complexity is not conducive to realistic use. Although the min sum algorithm (MSA) improves the computational convenience and applicability. It also weakens its decoding capability. In order to improve the decoding performance of MSA and exploit the potential, this paper propose an adaptive exponential correction factor. This can improve the decoding performance of MSA. Adaptive exponential min sum algorithm (AEMSA) demonstrate a noticeable improvement over the normalized min sum algorithm (NMSA) and the BP algorithm in high signal to noise ratio (SNR). AEMSA is also a simple, efficient, low power consuming and highly potential decoding algorithm that can be applied in hardware implementations.
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.