Quasi-cyclic LDPC codes for fast encoding

In this correspondence we present a special class of quasi-cyclic low-density parity-check (QC-LDPC) codes, called block-type LDPC (B-LDPC) codes, which have an efficient encoding algorithm due to the simple structure of their parity-check matrices. Since the parity-check matrix of a QC-LDPC code co...

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Bibliographic Details
Published in:IEEE transactions on information theory 2005-08, Vol.51 (8), p.2894-2901
Main Authors: MYUNG, Seho, YANG, Kyeongcheol, KIM, Jaeyoel
Format: Article
Language:English
Subjects:
Additive white noise
Algebra
Algorithms
Applied sciences
AWGN
Block cycle
Blocking
circulant permutation matrix
Codes
Coding, codes
Computer memory
Construction
Decoding
efficient encoding
Encoding
Exact sciences and technology
Floors
Gaussian noise
Hamming weight
Information, signal and communications theory
Linear programming
low-density parity-check (LDPC) codes
Mathematical analysis
Matrices
Matrix methods
Noise level
Parity check codes
Permutations
quasi-cyclic codes
Signal and communications theory
Telecommunications and information theory
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Summary:In this correspondence we present a special class of quasi-cyclic low-density parity-check (QC-LDPC) codes, called block-type LDPC (B-LDPC) codes, which have an efficient encoding algorithm due to the simple structure of their parity-check matrices. Since the parity-check matrix of a QC-LDPC code consists of circulant permutation matrices or the zero matrix, the required memory for storing it can be significantly reduced, as compared with randomly constructed LDPC codes. We show that the girth of a QC-LDPC code is upper-bounded by a certain number which is determined by the positions of circulant permutation matrices. The B-LDPC codes are constructed as irregular QC-LDPC codes with parity-check matrices of an almost lower triangular form so that they have an efficient encoding algorithm, good noise threshold, and low error floor. Their encoding complexity is linearly scaled regardless of the size of circulant permutation matrices.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2005.851753