Tree-Based Construction of LDPC Codes Having Good Pseudocodeword Weights

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dc.creatorKelley, Christine
dc.creatorSridhara, Deepak
dc.creatorRosenthal, Joachim
dc.date2005-10-03
dc.date2006-11-30
dc.date.accessioned2026-07-07T08:15:41Z
dc.date.available2026-07-07T08:15:41Z
dc.descriptionWe present a tree-based construction of LDPC codes that have minimum pseudocodeword weight equal to or almost equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a $d$-regular tree for a fixed number of layers and employing a connection algorithm based on permutations or mutually orthogonal Latin squares to close the tree. Methods are presented for degrees $d=p^s$ and $d = p^s+1$, for $p$ a prime. One class corresponds to the well-known finite-geometry and finite generalized quadrangle LDPC codes; the other codes presented are new. We also present some bounds on pseudocodeword weight for $p$-ary LDPC codes. Treating these codes as $p$-ary LDPC codes rather than binary LDPC codes improves their rates, minimum distances, and pseudocodeword weights, thereby giving a new importance to the finite geometry LDPC codes where $p > 2$.
dc.descriptionSubmitted to Transactions on Information Theory. Submitted: Oct. 1, 2005; Revised: May 1, 2006, Nov. 25, 2006
dc.identifierhttps://arxiv.org/abs/cs/0510009
dc.identifierhttp://arxiv.org/abs/cs/0510009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/133525
dc.subjectInformation Theory
dc.titleTree-Based Construction of LDPC Codes Having Good Pseudocodeword Weights
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