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Quotients of Gaussian graphs and their application to perfect codes
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Edge transitive ramanujan graphs and symmetric LDPC good codes
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Flexible LDPC decoder architectures
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Operation reduced low-density parity-check decoding algorithms for low power communication systems
International Journal of Communication Systems
Analysis of the relation between properties of LDPC codes and the tanner graph
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LP decoding of codes with expansion parameter above 2/3
Information Processing Letters
A class of quantum low-density parity check codes by combining seed graphs
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Linear-time decoding of regular expander codes
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Digital Signal Processing
Hi-index | 754.84 |
A method is described for constructing long error-correcting codes from one or more shorter error-correcting codes, referred to as subcodes, and a bipartite graph. A graph is shown which specifies carefully chosen subsets of the digits of the new codes that must be codewords in one of the shorter subcodes. Lower bounds to the rate and the minimum distance of the new code are derived in terms of the parameters of the graph and the subeodes. Both the encoders and decoders proposed are shown to take advantage of the code's explicit decomposition into subcodes to decompose and simplify the associated computational processes. Bounds on the performance of two specific decoding algorithms are established, and the asymptotic growth of the complexity of decoding for two types of codes and decoders is analyzed. The proposed decoders are able to make effective use of probabilistic information supplied by the channel receiver, e.g., reliability information, without greatly increasing the number of computations required. It is shown that choosing a transmission order for the digits that is appropriate for the graph and the subcodes can give the code excellent burst-error correction abilities. The construction principles