Tree-based construction of LDPC codes having good pseudocodeword weights

Christine A. Kelley, Deepak Sridhara, Joachim Rosenthal

Research output: Contribution to journalArticle

5 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1460-1478
Number of pages19
JournalIEEE Transactions on Information Theory
Volume53
Issue number4
DOIs
StatePublished - Apr 1 2007

Keywords

  • Iterative decoding
  • Low-density parity-check (LDPC) codes
  • Min-sum iterative decoding
  • P-ary pseudoweight
  • Pseudocodewords

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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