???????????? ???????????? ????????? LDPC ?????? ?????? ??????

?????????

Published May 1, 2012• 0 citations

Abstract

??? ??????????????? ???????????? ???????????? ????????? LDPC ?????? ?????? ????????? ????????????. ?????? ?????? ?????? ?????? ???????????? ???????????? ???????????? ????????? ?????? ???????????? ???????????? ????????? ?????? ?????? LDPC ?????? ????????? ????????????. ????????? LDPC ????????? ???????????? Tanner ???????????? ????????? ?????? ????????? ????????? LDPC ???????????? ???????????? ????????? ????????? ?????? ?????? ?????? ????????? ????????????. ?????? ?????????????????? ???????????? ???????????? ????????? LDPC ?????? ?????? ????????? ????????? ???????????? ??? ?????? ?????? ?????? ?????? ????????? ???????????????. ???????????? LDPC ????????? ????????? ???????????? ???-????????? ??? ???-?????? ??? ?????? ??? ?????? ?????? ??????????????? ????????? ????????? ?????? ?????? ??? ?????? ????????? ????????? ????????? ??? ?????????.

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???????????? ???????????? ????????? LDPC ?????? ?????? ??????

?????????

Published May 1, 2012• 0 citations

OpenAlex

Abstract

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13p

for

p

being a prime of the form

(39m+1)

. First, the cycle structure of Tanner (3, 13) QC-LDPC codes is analyzed, and the cycles of length lesser than 12 are divided into five equivalent classes. Based on each equivalent class, the existence of the cycles is equivalent to the solution of polynomial equations in a 39th unit root in the prime filed

\mathbb {F}_{p}

. By solving these polynomial equations over

\mathbb {F}_{p}

and summarizing the resulting candidate prime values, the girth of Tanner (3, 13) QC-LDPC codes is obtained. As an advantage, Tanner (3, 13) QC-LDPC codes have much higher code rates than Tanner (3, 5), (3, 7), (3, 11), and (5, 7) QC-LDPC codes, and provide a promising coding scheme for the data storage systems and optical communications.

Tanner

(J,L)

Quasi-Cyclic LDPC Codes: Girth Analysis and Derived Codes

(J,L)

QC-LDPC codes where

J

and

L

can be any two positive integers. According to the sufficient and necessary conditions for the existence of cycles of lengths 4, 6, 8, and 10, we propose an algorithm to determine the girth of Tanner

(J,L)

QC-LDPC codes with finite code lengths. Through the analysis of the obtained girth values, we generalize the laws of the girth distributions of Tanner

(J,L)

QC-LDPC codes. Furthermore, based on the exponent matrices of Tanner

(J,L)

QC-LDPC codes with known girths, we employ the column selection method and/or the masking technique to construct binary/nonbinary LDPC codes. The numerical results show that the constructed LDPC codes have good performance under iterative decoding over the additive white Gaussian noise channel.