Volume 2, Issue 3, November 2014, Page: 22-34
A Method of Constructing the Half-Rate QC-LDPC Codes with Linear Encoder, Maximum Column Weight Three and Inevitable Girth 26
Li Peng, Wuhan National Laboratory for Optoelectronics, School of Electronic Information and Communications in Huazhong University of Science and Technology, Wuhan, China, 430074
Received: Dec. 14, 2014;       Accepted: Dec. 28, 2014;       Published: Jan. 14, 2015
DOI: 10.11648/j.com.20140203.11      View  4046      Downloads  196
Abstract
This paper presents a method of constructing the half-rate irregular quasi-cyclic low-density parity-check codes which can provide linear encoding algorithm and their H-matrices may contain almost the least “1” elements comparing with H-matrices of all existing LDPC codes. This method shows that three kinds of special structural matrices, respectively named as S-matrix, M-matrix and A-matrix, are defined and constructed. With regard to the arbitrary large structural girth based on A-matrix, its general pattern is conceived and its basic rule is proved. A general method of constructing M-matrix with the inevitable girth larger than 24 is introduced by using generalized block design and treating A-matrix as its sub-matrix. S-matrix is generated by substituting specially circular-shift values for non-zero elements in M-matrix. Combining Hd-matrix generated from lifting the S-matrix and Hp-matrix with the approximate lower triangular array structure forms the H-matrix, i.e. H=[Hd Hp], which defines a class of half-rate irregular QC-LDPC codes with maximum column weight 3 and inevitable girth of length 26. Simulation tests show that the performance of the presented QC-LDPC code can achieve the signal-noise-ratio of below 2dB at the bit-error-rate of 10-5, which is comparable with the performance of the practical QC-LDPC codes in industrial Standard, but the complication of the former owing to the least “1” elements in H-matrix is lower than that of the later, as well as the storage requirement is smaller.
Keywords
Quasi-Cycle Low-Density Parity-Check (QC-LDPC) Code, Sparse Parity-Check Matrix, Girth, Generalized Block Design
To cite this article
Li Peng, A Method of Constructing the Half-Rate QC-LDPC Codes with Linear Encoder, Maximum Column Weight Three and Inevitable Girth 26, Communications. Vol. 2, No. 3, 2014, pp. 22-34. doi: 10.11648/j.com.20140203.11
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