On the number of errors correctable with codes on graphs

Alexander Barg, Arya Mazumdar

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) constructed from random graphs and fixed local constrained codes, and their extension to codes on hypergraphs. It is known that the average minimum distance of codes in these ensembles grows linearly with the code length. We show that these codes can correct a linearly growing number of errors under simple iterative decoding algorithms. In particular, we show that this property extends to codes constructed by parallel concatenation of Hamming codes and other codes with small minimum distance. Previously known results that proved this property for graph codes relied on graph expansion and required the choice of local codes with large distance relative to their length.

Original languageEnglish (US)
Article number5695098
Pages (from-to)910-919
Number of pages10
JournalIEEE Transactions on Information Theory
Volume57
Issue number2
DOIs
StatePublished - Feb 2011

Keywords

  • Graph codes
  • hypergraph codes
  • iterative decoding
  • parallel concatenation of codes

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