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International Conference on Aviation Safety and Information Technology (ICASIT)

A Double Modified Normalized Minimum Sum LDPC Decoding Algorithm

Taiyun Ding, Jie Li, Zhongyang Wei

Published Oct 14, 2020• 0 citations

Abstract

The NMS algorithm is most commonly used in the design of LDPC code decoders. The result of the smallest-sub-smallest operation in the minimum sum algorithm is actually only two values. According to this feature, this paper proposes an algorithm that uses two correction factors to normalize and correct the minimum value and the second minimum value. The normalized minimum sum algorithm have two correction factors λ1 and λ2, where λ1 normalizes the second smallest value, and λ2 normalizes the minimum value. Both the DN-MS algorithm and the NMS algorithm are approximate forms of the logarithmic domain BP algorithm, and have exactly the same amount of calculation. But the calculation result of the check node in the DN-MS algorithm is closer to the check node in the log domain BP algorithm, so it has better decoding performance.

DOI: 10.1145/3434581.3434663

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The NMS algorithm is most commonly used in the design of LDPC code decoders. The result of the smallest-sub-smallest operation in the minimum sum algorithm is actually only two values. According to this feature, this paper proposes an algorithm that uses two correction factors to normalize and correct the minimum value and the second minimum value. The normalized minimum sum algorithm have two correction factors λ1 and λ2, where λ1 normalizes the second smallest value, and λ2 normalizes the minimum value. Both the DN-MS algorithm and the NMS algorithm are approximate forms of the logarithmic domain BP algorithm, and have exactly the same amount of calculation. But the calculation result of the check node in the DN-MS algorithm is closer to the check node in the log domain BP algorithm, so it has better decoding performance.

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.

This paper proposes a low-complexity LDPC decoding algorithm with simplified check nodes updating. The proposed algorithm simplifies the result of the second-minimum in check nodes based on the first-minimum computation instead of computing it directly. In order to obtain the approximate result, effective corrected coefficients are utilized, which can reduce the complexity by eliminating the complex computations. Complexity analysis is provided and the results indicate that the complexity of the proposed algorithm is much lower than the general NMS algorithm and MS-based simplified algorithms. Simulation results show that the performance of the proposed algorithm can closely match the NMS algorithm with the same number of iterations.

In this paper, a modified min-sum decoding algorithm based on classified correction is proposed for low density parity check (LDPC) codes. Different from the single correction in the normalized belief propagation (BP)-based and offset BP-based algorithms [4], the proposed algorithm utilizes two corrections for both minimum and sub-minimum magnitudes of input messages in check nodes. These two correction factors can be obtained by analyzing the offset of updated messages in check nodes between the BP and the min-sum algorithms associated with check node degree. Simulation results show that the proposed algorithm can achieve performance very close to that of the BP algorithm. Furthermore, the FPGA implementation of this algorithm can reach a throughput of 200 Mbps at BER=10-6with lower complexity and fewer resources than the BP 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.