Tree-Based Construction of LDPC Codes Having Good Pseudocodeword Weights
Kelley, C.A.
Sridhara, D.
Rosenthal, J.
Dept. of Math., Notre Dame Univ., IN;
This paper appears in: Information Theory, IEEE Transactions on
Publication Date: April 2007
Volume: 53,
Issue: 4
On page(s): 1460-1478
ISSN: 0018-9448
INSPEC Accession Number: 9381937
Digital Object Identifier: 10.1109/TIT.2007.892774
Current Version Published: 2007-03-26
Abstract
We present a tree-based construction of low-density parity-check (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=ps and d=ps+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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