Paper Info
Title
Cyclic and Quasi-Cyclic LDPC Codes on Row and Column Constrained Parity-Check Matrices and Their Trapping Sets
Abstract
This paper is concerned with construction and structural analysis of both cyclic and quasi-cyclic codes, particularly LDPC codes. It consists of three parts. The first part shows that a cyclic code given by a parity-check matrix in circulant form can be decomposed into descendant cyclic and quasi-cyclic codes of various lengths and rates. Some fundamental structural properties of these descendant codes are developed, including the characterizations of the roots of the generator polynomial of a cyclic descendant code. The second part of the paper shows that cyclic and quasi-cyclic descendant LDPC codes can be derived from cyclic finite geometry LDPC codes using the results developed in first part of the paper. This enlarges the repertoire of cyclic LDPC codes. The third part of the paper analyzes the trapping sets of regular LDPC codes whose parity-check matrices satisfy a certain constraint on their rows and columns. Several classes of finite geometry and finite field cyclic and quasi-cyclic LDPC codes with large minimum weights are shown to have no harmful trapping sets with size smaller than their minimum weights. Consequently, their performance error-floors are dominated by their minimum weights.
Year
Venue
Keywords
2010
Clinical Orthopaedics and Related Research
cyclic code,finite field,satisfiability,structure analysis,information theory,ldpc code
Field
DocType
Volume
Discrete mathematics,Forward error correction,Combinatorics,Concatenated error correction code,Parity-check matrix,Low-density parity-check code,Polynomial code,Block code,Cyclic code,Linear code,Mathematics
Journal
abs/1012.3
Citations 
PageRank 
References 
5
0.53
39
Authors
4
Name
Order
Citations
PageRank
Qin Huang135534.55
Qiuju Diao21148.72
Shu Lin323416.88
Khaled A. S. Abdel-Ghaffar4616122.03