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Video Engineering

Improved Min-sum Algorithm with Low Complexity for Decoding LDPC Codes

Wu Ju

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

In order to reduce the performance loss of SMMS( Single-Minimum,Min-Sum) algorithm for decoding LDPC( LowDensity Parity-Check) codes,the ACMS( adaptive configurable Min-Sum) algorithm is proposed in this paper. Only the absolute minimum is used in this algorithm to update the check-node message and the second minimum is determined by a configurable estimation weight factor based on the iteration and a correction factor based on the number of error bits in each hard decision. Compared to the original SMMS and VWMS algorithm,the simulation result shows the proposed ACMS algorithm reduce the performance loss in general by introducing only a little additional complexity.

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•Oct 31, 2015•2 citations
In order to reduce the performance loss of SMMS( Single-Minimum,Min-Sum) algorithm for decoding LDPC( LowDensity Parity-Check) codes,the ACMS( adaptive configurable Min-Sum) algorithm is proposed in this paper. Only the absolute minimum is used in this algorithm to update the check-node message and the second minimum is determined by a configurable estimation weight factor based on the iteration and a correction factor based on the number of error bits in each hard decision. Compared to the original SMMS and VWMS algorithm,the simulation result shows the proposed ACMS algorithm reduce the performance loss in general by introducing only a little additional complexity.
The Minimum Sum (MS) algorithm is a standard Low-Density Parity-Check Codes (LDPC) decoding algorithm. Compared with traditional algorithms, it uses approximate calculations to reduce the computational complexity of the algorithm when calculating parity nodes, resulting in performance loss issues. To improve the LDPC decoding performance, the LDPC decoding algorithm of Multi-parameter Compensated Min-Sum (MCMS) is proposed. This algorithm introduces relevant information, such as channel and code length, into calculating update verification nodes. Introducing multiplication and correction factors to reduce errors in validation node calculations through multi-parameter compensation. Simulation results show that the MCMS algorithm has superior error rate performance compared with the MS 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.
Low-Density Parity-Check (LDPC) code is a linear block code approaching the Shannon limit. The improvement of the decoding performance of LDPC codes is a hot research direction today. To improve the decoding performance of the self-correcting min-sum (SCMS) algorithm, an improved self-correcting min-sum (ISCMS) algorithm is proposed based on this algorithm. In the iterative decoding process of the ISCMS algorithm, the update rule of the check node (CN) is optimized to the update rule of the CN of the IOMS algorithm, which improves the accuracy of decoding from the processing of the CN. Simulation results show that the proposed ISCMS algorithm has better error performance and convergence performance than the SCMS algorithm with a small increase in computational complexity.
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.
Low-density parity-check (LDPC) codes have attracted tremendous attention for their excellent error-correction performance and inherent fitness for high-parallelism implementation. With great complexity reduction and friendly for hardware implementation, the min-sum (MS) decoding algorithm for LDPC codes gains widespread applications in practical. In the MS decoding algorithm, finding the first two minima among input variable-to-check messages is the most complex part. To further reduce the complexity of the MS decoding algorithm, an efficient single-minimum (single-min) based layered MS decoding for quasi-cyclic LDPC (QC-LDPC) codes is proposed in this paper. It is found that statistically the difference between the first minimum and second minimum increases as the decoding becomes more convergent. Accordingly, in the proposed single-min scheme, the second minimum is approximately derived based on the first minimum and an index indicating the convergence degree. Besides, some other metrics that are easily obtained are used to refine the second minimum. Simulation results show that the proposed method can significantly improve the error-correction performance and lower the average number of iterations, compared with the state-of-the-art single-min based MS decoding algorithms.
Abstract ― Low Density Parity Check (LDPC) code approaches Shannon–limit performance for binary field and long code lengths. However, performance of binary LDPC code is degraded when the code word length is small. An optimized min-sum algorithm for LDPC code is proposed in this paper. In this algorithm unlike other decoding methods, an optimization factor has been introduced in both check node and bit node of the Min-sum algorithm. The optimization factor is obtained before decoding program, and the same factor is multiplied twice in one cycle. So the increased complexity is fairly low. Simulation results show that the proposed Optimized Min-Sum decoding algorithm performs very close to the Sum-Product decoding while preserving the main features of the Min-Sum decoding, that is low complexity and independence with respect to noise variance estimation errors.