Quasi-Cyclic LDPC Codes with Parity-Check Matrices of Column Weight Two or More for Correcting Phased Bursts of Erasures

Xin Xiao, Bane Vasic, Shu Lin, Juane Li, Khaled Abdel-Ghaffar

Research output: Contribution to journalArticlepeer-review

Abstract

In his pioneering work on LDPC codes, Gallager dismissed codes with parity-check matrices of weight two after proving that their minimum Hamming distances grow at most logarithmically with their code lengths. In spite of their poor minimum Hamming distances, it is shown that quasi-cyclic LDPC codes with parity-check matrices of column weight two have good capability to correct phased bursts of erasures which may not be surpassed by using quasi-cyclic LDPC codes with parity-check matrices of column weight three or more. By modifying the parity-check matrices of column weight two and globally coupling them, the erasure correcting capability can be further enhanced. Quasi-cyclic LDPC codes with parity-check matrices of column weight three or more that can correct phased bursts of erasures and perform well over the AWGN channel are also considered. Examples of such codes based on Reed-Solomon and Gabidulin codes are presented.

Original languageEnglish (US)
JournalIEEE Transactions on Communications
DOIs
StateAccepted/In press - 2021

Keywords

  • Erasure correction
  • Gabidulin code
  • global coupling
  • Golomb ruler
  • LDPC code
  • Linear codes
  • Maximum likelihood decoding
  • Parity check codes
  • phased burst
  • quasi-cyclic code
  • Redundancy
  • Reed-Solomon code
  • Reed-Solomon codes
  • Solids
  • Sparse matrices

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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