Tree-Based Construction of LDPC Codes Having Good Pseudocodeword Weights

Christine Kelley; Deepak Sridhara; Joachim Rosenthal

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Tree-Based Construction of LDPC Codes Having Good Pseudocodeword Weights

Christine Kelley·Deepak Sridhara·Joachim Rosenthal

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Abstract

We 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 $p > 2$.

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Christine Kelley, Deepak Sridhara, Joachim Rosenthal. 2006-11-30. Tree-Based Construction of LDPC Codes Having Good Pseudocodeword Weights. https://arxiv.org/abs/cs/0510009

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