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Full-Text Articles in Physical Sciences and Mathematics
Average Min-Sum Decoding Of Ldpc Codes, Nathan Axvig, Deanna Dreher, Katherine Morrison, Eric T. Psota, Lance C. Pérez, Judy L. Walker
Average Min-Sum Decoding Of Ldpc Codes, Nathan Axvig, Deanna Dreher, Katherine Morrison, Eric T. Psota, Lance C. Pérez, Judy L. Walker
Department of Mathematics: Faculty Publications
Simulations have shown that the outputs of minsum (MS) decoding generally behave in one of two ways: the output either eventually stabilizes at a codeword or eventually cycles through a finite set of vectors that may include both codewords and non-codewords. This inconsistency in MS across iterations has significantly contributed to the difficulty in studying the performance of this decoder. To overcome this problem, a new decoder, average min-sum (AMS), is proposed; this decoder outputs the average of the min-sum output vectors over a finite set of iterations. Simulations comparing MS, AMS, linear programming (LP) decoding, and maximum likelihood (ML) …
A Universal Theory Of Pseudocodewords, Nathan Axvig, Emily Price, Eric T. Psota, Deanna Turk, Lance C. Pérez, Judy L. Walker
A Universal Theory Of Pseudocodewords, Nathan Axvig, Emily Price, Eric T. Psota, Deanna Turk, Lance C. Pérez, Judy L. Walker
Department of Mathematics: Faculty Publications
Three types of pseudocodewords for LDPC codes are found in the literature: graph cover pseudocodewords, linear programming pseudocodewords, and computation tree pseudocodewords. In this paper we first review these three notions and known connections between them. We then propose a new decoding rule — universal cover decoding — for LDPC codes. This new decoding rule also has a notion of pseudocodeword attached, and this fourth notion provides a framework in which we can better understand the other three.