This study is concerned with the application of non-binary low-density parity-check (nb-ldpc) codes to binary input inter-symbol interference channels. Two low-complexity joint detection/decoding algorithms are propos...
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This study is concerned with the application of non-binary low-density parity-check (nb-ldpc) codes to binary input inter-symbol interference channels. Two low-complexity joint detection/decoding algorithms are proposed. One is referred to as max-log-MAP/X-EMS algorithm, which is implemented by exchanging soft messages between the max-log-MAP detector and the extended min-sum (EMS) decoder. The max-log-MAP/X-EMS algorithm is applicable to general nb-ldpc codes. The other one, referred to as Viterbi/GMLGD algorithm, is designed in particular for majority-logic decodable nb-ldpc codes. The Viterbi/GMLGD algorithm works in an iterative manner by exchanging hard-decisions between the Viterbi detector and the generalised majority-logic decoder (GMLGD). As a by-product, a variant of the original EMS algorithm is proposed, which is referred to as mu-EMS algorithm. In the mu-EMS algorithm, the messages are truncated according to an adaptive threshold, resulting in a more efficient algorithm. Simulations results show that the max-log-MAP/X-EMS algorithm performs as well as the traditional iterative detection/decoding algorithm based on the BCJR algorithm and theQ-ary sum-product algorithm, but with lower complexity. The complexity can be further reduced for majority-logic decodable nb-ldpc codes by executing the Viterbi/GMLGD algorithm with a performance degradation within one dB. These algorithms provide good candidates for trade-offs between performance and complexity.
Non-binary low-density parity-check (nb-ldpc) codes can be directly constructed by using algebraic methods, or indirectly constructed by mapping well-designed binary parity-check matrices to non-binary parity-check ma...
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Non-binary low-density parity-check (nb-ldpc) codes can be directly constructed by using algebraic methods, or indirectly constructed by mapping well-designed binary parity-check matrices to non-binary parity-check matrices. Given the Tanner graph (TG) of a nb-ldpc code, the selection of edge weights in the TG significantly affects the performance of the nb-ldpc code. The authors introduce an edge weight distribution (EWD) parameter for the TG of nb-ldpc codes. By utilising particle swarm optimisation (PSO), the EWD is optimised and it has been demonstrated that the optimal EWD approaches a two-element distribution for large field size and high average variable-node degree. With the optimised EWD, the authors construct a class of field-compatible ldpc (FC-ldpc) codes over GF(q) whose parity-check matrices only include elements 0, 1 and 2, and can be encoded and decoded over different field sizes. The simulations demonstrate that the performance of the proposed FC-ldpccodes improves monotonically with increasing field size, and significantly outperforms that of the corresponding algebraic nb-ldpc codes or nb-ldpc codes generated with uniform distribution of non-zero elements over GF(q).
In this paper, we propose a weighted hard-reliability based one step majority-logic decoding algorithm for NON-Binary Low-Density Parity-Check (nb-ldpc) codes. To improve the information reliable of check nodes and th...
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ISBN:
(纸本)9781728101200
In this paper, we propose a weighted hard-reliability based one step majority-logic decoding algorithm for NON-Binary Low-Density Parity-Check (nb-ldpc) codes. To improve the information reliable of check nodes and the use efficiency of receive message, a weight reliability message method is proposed where only the weight values generated in the decoding initialization are reserved for the iterate decoding process. We also propose a new message reliability updating rule for each iterate decoding, in which only the unreliable variable nodes are updated. Simulation results show that our proposed weighted iterative hard-reliability (WIHRB) algorithm significantly improves the error-floor performance compared to the conventional truncate iterative hard-reliability (TIHRB) algorithms.
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