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The role of pseudocodewords in causing non-codeword outputs in linear programming decoding, graph cover decoding, and iterative message-passing decoding is investigated. The three main types of pseudocodewords in the literature-linear programming pseudocodewords, graph cover pseudocodewords, and computation tree pseudocodewords-are reviewed and connections between them are explored. Some discrepancies...
In this paper, the non-codeword errors was analyzed that occur during parallel, iterative decoding with the min-sum decoder. Recently, work has been done relating the min-sum decoder to the linear programming (LP) decoder via graph covers. The LP decoder recasts the problem of decoding as an optimization problem whose feasible set is a polytope defined by the parity-check matrix of a code. It was...
Simulations have shown that the outputs of min-sum (MS) decoding generally behave in one of two ways: either the output vector eventually stabilizes at a codeword or it eventually cycles through a finite set of vectors that may include both codewords and non-codewords. The latter behavior has significantly contributed to the difficulty in studying the performance of this decoder. To overcome this...
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