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IEEE Communications Letters

A combining method of quasi-cyclic LDPC codes by the Chinese remainder theorem

Seho Myung, Kyeongcheol Yang

Published Sep 1, 2005• 48 citations
Publisher

Abstract

In this paper we propose a method of constructing quasi-cyclic low-density parity-check (QC-LDPC) codes of large length by combining QC-LDPC codes of small length as their component codes, via the Chinese remainder theorem. The girth of the QC-LDPC codes obtained by the proposed method is always larger than or equal to that of each component code. By applying the method to array codes, we present a family of high-rate regular QC-LDPC codes with no 4-cycles. Simulation results show that they have almost the same performance as random regular LDPC codes.

DOI
10.1109/lcomm.2005.1506715

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IEEE Communications Letters•May 1, 2008•20 citations
In this paper we propose a method of constructing quasi-cyclic low-density parity-check (QC-LDPC) codes of large length by combining QC-LDPC codes of small length as their component codes, via the Chinese remainder theorem. The girth of the QC-LDPC codes obtained by the proposed method is always larger than or equal to that of each component code. By applying the method to array codes, we present a family of high-rate regular QC-LDPC codes with no 4-cycles. Simulation results show that they have almost the same performance as random regular LDPC codes.
An improved combining method for designing quasi- cyclic low- density parity- check( QC-LDPC) codes based on Chinese Remainder Theorem( CRT) is proposed to improve the error- correcting performance by increasing the girth and decreasing the number of short cycles. With the CRT combining method,the difficult problem of designing QC- LDPC codes with girth g is translated into a task of designing one component code with girth g. By properly permuting the column blocks of parity- check matrices of other component codes,a lot of QC- LDPC codes with much shorter cycles and better performance can be designed,which are more suitable for communication systems with request of high reliability. Simulations show that compared with existing CRT- based QC- LDPC codes,the proposed QC- LDPC codes have much shorter cycles and obtain 1. 2 d B coding gain at bit error rate( BER) of 10- 6.
In this letter, we consider two problems associated with quasi-cyclic low-density parity-check (QC-LDPC) codes. The first is how to extend the code length of a QC-LDPC code without reducing the girth. The second is how to design a QCLDPC code with a prescribed girth easily. We deal with these two problems by using a combining method of QC-LDPC codes via the Chinese Remainder Theorem (CRT). Codes constructed with our proposed method have flexible code lengths, flexible code rates and large girth. Simulation results show that they perform very well with the iterative decoding.
An improved combining method is proposed for constructing quasi‐cyclic low‐density parity‐check (QC‐LDPC) codes with large girth and few short cycles. Large girth QC‐LDPC codes can be obtained by carefully designing one component code with large girth. By properly designing the other component codes, a lot of QC‐LDPC codes with very few short cycles can be designed. Simulations show that compared with Chinese remainder theorem based QC‐LDPC codes and progressive edge‐growth based QC‐LDPC codes, the proposed QC‐LDPC codes have much less short cycles and better performance.
Quasi-Cyclic LDPC (QC-LDPC) codes are widely accepted as a standard for various wireless communication systems in the present and are recommended for future applications. Girth is an important parameter for designing a good general class of LDPC codes. However, obtaining high girth for a parity-check matrix requires lot of computational and structural complexities. To reduce the complexity, this paper proposes to combine the exponent matrices of QC-LDPC codes using the Chinese Remainder Theorem. Simulation results show that a high girth large block-length QC-LDPC code can be obtained from less girth component of QC-LDPC codes.
A generalization of the Chinese Remainder Theorem (CRT) combining method is proposed to design much more and better quasi-cyclic (QC) LDPC codes when the parity check matrices of the component codes are given. It can design a much larger class of QC-LDPC codes with similar performance by loosening the condition for determining the intermediate parameters. By permuting the block rows of the parity check matrices of the component codes, a lot of QC-LDPC codes with much less 6-cycles and better performance can be designed. At a BER of 10-6some QC-LDPC codes designed by the generalized combining method outperform those designed by the CRT combining method by 0.5 dB.