KA
KAS Abdel-Ghaffar
27 records found
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The Cadambe-Mazumdar bound gives a necessary condition for a code to have a certain locality in case of a single erasure in terms of length, dimension, and Hamming distance of the code and of certain shortened codes. The bound has been generalized by Rawat, Mazumdar, and Vishwana
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Linear block codes over noisy channels causing both erasures and errors can be decoded by deleting the erased symbols and decoding the resulting vector with respect to a punctured code and then retrieving the erased symbols. This can be accomplished using separating parity-check
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Stopping sets, and in particular their numbers and sizes play an important role in determining the performance of iterative decoders of linear codes over binary erasure channels. In the 2004 Shannon Lecture, McElievve presented ans expression for the number of stopping sets of si
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The generalized iterative decoding concept offers attractive performances versus complexity trade-off oppurtunities in the spectrum between traditional iteratieve decoding and optimal decoding for linear block codes over the binary erasure channel. In each iteration, a system of
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Iterative techniques have been proposed for decoding linear binary block codes over erasure channels. The performance of such decoding techniques depends on the parity-check matrices used, and in partivular, on the numbers and sizes of stopping sets of these matrices. In the 2004
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It has been claimed that the performance of a linear block code under iterative decoding on the binary erasure channel is determined by the stoppin gdistance, i.e., the size of hte smallest non-empty stopping set in the associated Tanner graph. Indeed, this is true from the persp
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The performance of iterative decoding techniques for linear block codes correcting erasures depends very much on the sizes of the stopping sets associated with the underlying Tanner graph, or equivalently, the parity-check matrix representing the code. In this paper, we introduce
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In the 2004 Shanna Lecture, McEliece presented an expression for the number of stopping sets of size three for a full-rank parity-check matrix of the Hamming code. In this paper, we derive an expression for the number of stopping sets of any given size for the same parity-check m
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