On the girth of tanner (3, 5) quasi-cyclic LDPC codes

In this correspondence, the cycles of Tanner (3,5) quasi-cyclic (QC) low-density parity-check (LDPC) codes are analyzed and their girth values are derived. The conditions for the existence of cycles of lengths 4,6,8, and 10 in Tanner (3,5) QC LDPC codes of length 5p are expressed in terms of polynom...

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Bibliographic Details
Published in:IEEE transactions on information theory 2006-04, Vol.52 (4), p.1739-1744
Main Authors: KIM, Sunghwan, NO, Jong-Seon, HABONG CHUNG, SHIN, Dong-Joon
Format: Article
Language:English
Subjects:
Additive white noise
Applied sciences
AWGN
Coding, codes
Computer science
Decoding
Equations
Exact sciences and technology
Filled plastics
Girth
Information theory
Information, signal and communications theory
low-density parity-check (LDPC) codes
Mathematical analysis
Parity check codes
Polynomials
Quality control
Quantum cascade lasers
quasi-cyclic (QC) codes
Roots
Shift registers
Signal and communications theory
Telecommunications and information theory
Unity
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Summary:In this correspondence, the cycles of Tanner (3,5) quasi-cyclic (QC) low-density parity-check (LDPC) codes are analyzed and their girth values are derived. The conditions for the existence of cycles of lengths 4,6,8, and 10 in Tanner (3,5) QC LDPC codes of length 5p are expressed in terms of polynomial equations in a 15th root of unity of the prime field F/sub p/. By checking the existence of solutions for these equations over F/sub p/, the girths of Tanner (3,5) QC LDPC codes are derived.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2006.871060