Open AccessReed-Solomon Based Quasi-Cyclic LDPC Codes: Designs, Girth, Cycle Structure, and Reduction of Short Cycles
Author(s) -
Xin Xiao,
Bane Vasić,
Shu Lin,
Khaled Abdel-Ghaffar,
W.E. Ryan
Publication year - 2019
Publication title -
ieee transactions on communications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.468
H-Index - 214
eISSN - 1558-0857
pISSN - 0090-6778
DOI - 10.1109/tcomm.2019.2916605
Subject(s) - low density parity check code , turbo code , concatenated error correction code , serial concatenated convolutional codes , reed–solomon error correction , tornado code , block code , mathematics , tanner graph , reed–muller code , girth (graph theory) , linear code , forward error correction , raptor code , algorithm , discrete mathematics , decoding methods
Designs and constructions of quasi-cyclic (QC) LDPC codes for the AWGN channel are presented. The codes are constructed based on the conventional parity-check matrices of Reed–Solomon (RS) codes and are referred to as RS-QC-LDPC codes. Several classes of RS-QC-LDPC codes are given. Cycle structural properties of the Tanner graphs of codes in these classes are analyzed and specific methods for constructing codes with girth at least eight and reducing their short cycles are presented. The designed codes perform well in both waterfall and low error-rate regions.
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