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When non-binary low-density parity-check (NB-LDPC) codes with low column weights are adopted, the iterative reliability-based majority-logic decoding (IRB-MLGD) algorithms suffer from severe performance degradation compared to message passing algorithms. In this brief, based on the improved iterative soft reliability-based (IISRB)-MLGD algorithm, we propose a perturbation-injected (P)-IISRB algorithm, where a regular perturbation is introduced to alleviate the periodic point problem that is the main reason for IISRB decoding failure. Compared with the conventional IISRB, the new algorithm significantly improves the decoding performance, lowering the error-floor by at least two orders of magnitude for the example code. Besides, instead of traditionally pre-computing and storing all the $q$ -ary channel reliability measures, a real-time computing method is presented, which reduces the memory cost from $\mathcal {O}$ ($q$) to $\mathcal {O}$ ($\log _{2}q$). [ABSTRACT FROM AUTHOR]

This paper presents bit-reliability based majority-logic decoding (MLgD) algorithms for non-binary LDPC codes. The proposed algorithms pass only one Galois field element and its reliability along each edge of the Tanner graph of a non-binary LDPC code. Since their reliability updates are in terms of bits rather than symbols, they are more efficient than traditional MLgD based decoding algorithms. By weighting the soft reliability of the extrinsic information-sums based on their hard reliability, the proposed algorithms can achieve good error performance for non-binary LDPC codes with various column weights. Moreover, their computational complexity and memory consumption are remarkably reduced compared with existing MLgD based decoding algorithms. As a result, they provide effective tradeoffs between error performance and complexity for decoding of non-binary LDPC codes. [ABSTRACT FROM AUTHOR]

Short-length Reed—Muller codes under majority-logic decoding are of particular importance for efficient hardware implementations in real-time and embedded systems. This paper significantly improves Chen's two-step majority-logic decoding method for binary Reed—Muller codes RM(r,m), r ≤ m/2, if — systematic encoding assumed — only errors at information positions are to be corrected. Some general results on the minimal number of majority gates are presented that are particularly good for short codes. Specifically, with its importance in applications as a 3-error-correcting, self-dual code, the smallest non-trivial example, RM(2,5) of dimension 16 and length 32, is investigated in detail. Further, the decoding complexity of our procedure is compared with that of Chen's decoding algorithm for various Reed—Muller codes up to length 2^10. [ABSTRACT FROM AUTHOR]