Journal Article10.1109/TCOMM.2016.2609906
Structural Analysis of Array-Based Non-Binary LDPC Codes
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TL;DR: It is shown that there may exist codewords with symbol weight four, six, and seven in array-based NBLDPC codes defined by parity-check matrices with column weight two and that the graphical substructure induced by a weight-7 codeword takes the graphical subgraph induced by the related weight-6codewords as a subgraph.
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Abstract: Structural properties of array-based non-binary low-density parity-check (NBLDPC) codes are studied in this paper. First, we characterize graphical substructures induced by codewords of symbol weight six in array-based NBLDPC codes defined by parity-check matrices with column weight three. We also reveal necessary conditions for these graphical substructures to incur weight-6 codewords. Such conditions can be used to select nonzero elements for avoiding weight-6 codewords or reducing the multiplicity of weight-6 codewords. Second, we show that there exist weight-7 codewords in array-based NBLDPC codes defined by parity-check matrices with column weight three. As a byproduct, we find that the graphical substructure induced by a weight-7 codeword takes the graphical substructure induced by the related weight-6 codewords as a subgraph. Third, we show that there may exist codewords with symbol weight four, six, and seven in array-based NBLDPC codes defined by parity-check matrices with column weight two. These results enrich the structural analysis of array-based LDPC codes. In addition, simulation results show the performance advantage of array-based NBLDPC codes.
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Citations
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Extended construction of array-based non-binary LDPC codes
Shancheng Zhao,Xiao Ma +1 more
TL;DR: The authors extend the array- based construction to composite numbers to give an explicit construction of structured array-based NB LDPC codes with column weights three, four, and five, which perform as well as the random codes constructed by progressive edge-growth algorithm, when decoded with the Q-ary sum product algorithm and the low-complexity weighted bit-reliability-based decoding algorithm.
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Nonbinary LDPC cycle codes: efficient search, design, and code optimization
TL;DR: Nonbinary low-density parity-check (NBLDPC) codes have the ability of approaching capacity when decoded iteratively using a probabilistic decoding algorithm, and with the increase of the finite field size q, NBLD PC codes over GF(q) have much better performance under iterative decoding for a constant code length.
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Structural analysis of array-based non-binary LDPC codes
Shancheng Zhao,Xiujie Huang,Xiao Ma +2 more
- 01 Sep 2016
TL;DR: It is shown that there may exist codewords with symbol weight four, six, and seven in array-based NBLDPC codes defined by parity-check matrices with column weight two and that the graphical substructure induced by a weight-7 codeword takes the graphical subgraph induced by the related weight-6codewords as a subgraph.
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