High-rate nonbinary regular ouasi-cyclic LDPC codes for optical communications

Murat Arabaci, Ivan B Djordjevic, Ross Saunders, Roberto M. Marcoccia

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

The parity-check matrix of a nonbinary (NB) low-density parity-check (LDPC) code over Galois field (q) is constructed by assigning nonzero elements from (q) to the 1s in corresponding binary LDPC code. In this paper, we state and prove a theorem that establishes a necessary and sufficient condition that an NB matrix over (q), constructed by assigning nonzero elements from (q) to the 1s in the parity-check matrix of a binary quasi-cyclic (QC) LDPC code, must satisfy in order for its null-space to define a nonbinary QC-LDPC (NB-QC-LDPC) code. We also provide a general scheme for constructing NB-QC-LDPC codes along with some other code construction schemes targeting different goals, e.g., a scheme that can be used to construct codes for which the fast-Fourier-transform-based decoding algorithm does not contain any intermediary permutation blocks between bit node processing and check node processing steps. Via Monte Carlo simulations, we demonstrate that NB-QC-LDPC codes can achieve a net effective coding gain of 10.8 dB at an output bit error rate of 10-12. Due to their structural properties that can be exploited during encoding/decoding and impressive error rate performance, NB-QC-LDPC codes are strong candidates for application in optical communications.

Original languageEnglish (US)
Pages (from-to)5261-5267
Number of pages7
JournalJournal of Lightwave Technology
Volume27
Issue number23
DOIs
StatePublished - Dec 1 2009

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optical communication
parity
decoding
coding
matrices
permutations
bit error rate
theorems
output

Keywords

  • Low-density parity-check (LDPC) codes
  • Optical communications
  • Quasi-cyclic (QC) codes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

High-rate nonbinary regular ouasi-cyclic LDPC codes for optical communications. / Arabaci, Murat; Djordjevic, Ivan B; Saunders, Ross; Marcoccia, Roberto M.

In: Journal of Lightwave Technology, Vol. 27, No. 23, 01.12.2009, p. 5261-5267.

Research output: Contribution to journalArticle

Arabaci, Murat ; Djordjevic, Ivan B ; Saunders, Ross ; Marcoccia, Roberto M. / High-rate nonbinary regular ouasi-cyclic LDPC codes for optical communications. In: Journal of Lightwave Technology. 2009 ; Vol. 27, No. 23. pp. 5261-5267.
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