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IEEE Transactions on Communications

Minimum-Set Min-Sum Decoding Algorithms for Non-Binary LDPC Codes

Zhanxian Liu, Haijun Zhang, Jiahao Huo, Ning Wang

Published Aug 27, 2024• 1 citation
Publisher

Abstract

During the check node (CN) update, the elements of input message vectors are redundant for the output message vectors. Hence, in this paper, we exactly select from the input message vectors the elements, which really have contributions to the error-correction performance and constitute the minimum set for the CN update. With adoption of the forward and backward (FB) scheme, an adaptive minimum-set min-sum algorithm (AMSA) is proposed to reduce the computation complexity of the FB process. In order to concurrently update the output vectors belonging to the same CN, we present a parallel minimum-set min-sum algorithm (PMSA) with lower memory complexity than the AMSA. Compared with the min-sum algorithms, the two proposed minimum-set based algorithms introduce no error performance loss.

DOI
10.1109/tcomm.2024.3450606

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During the check node (CN) update, the elements of input message vectors are redundant for the output message vectors. Hence, in this paper, we exactly select from the input message vectors the elements, which really have contributions to the error-correction performance and constitute the minimum set for the CN update. With adoption of the forward and backward (FB) scheme, an adaptive minimum-set min-sum algorithm (AMSA) is proposed to reduce the computation complexity of the FB process. In order to concurrently update the output vectors belonging to the same CN, we present a parallel minimum-set min-sum algorithm (PMSA) with lower memory complexity than the AMSA. Compared with the min-sum algorithms, the two proposed minimum-set based algorithms introduce no error performance loss.
This paper reduces the complexity of decoding non-binary low-density parity-check (LDPC) codes by set partition. In the check node update, the input vectors are partitioned into several sets such that different elements in the virtual matrix enjoy various computational strategies. As a result, the proposed algorithm achieves high computational efficiency by setting strategies according to the correct probability of these elements. Simulation results indicate that it significantly decreases the complexity of check node update with negligible performance loss.
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.
Non-binary low-density parity-check (NB-LDPC) codes are robust to various channel impairments. In this paper, we present a new decoding algorithm for the NB-LDPC decoder that is based on the q-ary min-sum algorithm (QMSA). The new one modifies the check node (CN) computations of the QMSA into two steps. By reorganizing the message entries and providing the most likely symbol, a compressed intermediate message can be easily obtained and stored, from which the check-to-variable messages can be computed with a look-up table. Thus the decoder architecture can have a straightforward design for the CN with reduced complexity and memory requirements. Besides, the simulation results demonstrate that the proposed algorithm has negligible performance loss compared to the QMSA over AWGN channel.
Non-binary low-density parity-check (NB-LDPC) codes can achieve higher coding gain than binary LDPC codes when the code length is moderate at the cost of higher complexity. One major step of NB-LDPC decoding is check node processing. Previously, iterative forward-backward approaches are employed to implement this step. However, the storage of the intermediate results of the forward and backward computations requires large memory. In this paper, a novel check node processing scheme and corresponding VLSI architectures are proposed for the extended Min-sum NB-LDPC decoding. The proposed scheme only stores a limited number of sorted variable-to-check messages. Then the check-to-variable messages for different variable node are generated independently. For a (837, 726) NB-LDPC code over GF(25), the proposed architecture only requires 64% of the area of the previous design with the same throughput and error-correcting performance.
Although non-binary low-density parity-check (NB-LDPC) codes have better error-correction capability than that of binary LDPC codes, their decoding complexity is significantly higher.Therefore, it is crucial to reduce the decoding complexity of NB-LDPC while maintaining their error-correction capability to adopt them for various applications.The extended min-sum (EMS) algorithm is widely used for decoding NB-LDPC codes, and it reduces the complexity of check node (CN) operations via message truncation.Herein, we propose a low-cost CN processing method to reduce the complexity of CN operations, which take most of the decoding time.Unlike existing studies on low complexity CN operations, the proposed method employs quick selection algorithm, thereby reducing the hardware complexity and CN operation time.The experimental results show that the proposed selection-based CN operation is more than three times faster and achieves better error-correction performance than the conventional EMS algorithm.
In the check node (CN) update of non-binary message-passing algorithms, each element of reliability vectors takes the same computational complexity. However, our analysis indicates that various elements in the same vector have various correct probabilities, thus have different contributions to error performance. In order to match computational complexity with correct probability, all elements in a vector are partitioned into different sets. For the extended min-sum (EMS) decoding, various strategies are applied for sets according to their correct probability. For the trellis-based EMS decoding, it is interesting that set partition only involves fixed paths, thus it does not need to search over the whole trellis of a CN. Complexity analysis and simulation results show that the proposed algorithms efficiently decode non-binary low-density parity-check codes, including ultra-sparse ones.