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IEEE Communications Letters

Lifting methods for quasi-cyclic LDPC codes

Seho Myung, Kyeongcheol Yang, Young‐Kyun Kim

Published Jun 1, 2006• 36 citations
Publisher

Abstract

In this paper, we present two simple methods to construct a quasi-cyclic LDPC (QC-LDPC) code of larger length by lifting a given QC-LDPC code. We show that its girth is always larger than or equal to that of the given QC-LDPC code. Applying the methods recursively, it is possible to construct a sequence of QC-LDPC codes generated from a single exponent matrix by proper floor or modulo operations. Simulation results show that they have no serious performance degradation, as compared with randomly constructed LDPC codes

DOI
10.1109/lcomm.2006.1638625

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In this paper, we present two simple methods to construct a quasi-cyclic LDPC (QC-LDPC) code of larger length by lifting a given QC-LDPC code. We show that its girth is always larger than or equal to that of the given QC-LDPC code. Applying the methods recursively, it is possible to construct a sequence of QC-LDPC codes generated from a single exponent matrix by proper floor or modulo operations. Simulation results show that they have no serious performance degradation, as compared with randomly constructed LDPC codes
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In this letter, we present an efficient method for constructing a family of quasi-cyclic low-density parity-check (QC-LDPC) codes specified only by one single exponent matrix that can support multiple lifting sizes. Our method adopts the small-lifting-size-first design strategy and the resulting exponent matrix of larger lifting size has non-decreasing girth. Numerical results show that all constituent codes can perform as well as (outperform) the CCSDS (5G) LDPC codes over the AWGN channel with the iterative decoding algorithms. This fact demonstrates the feasibility and validity of our proposed method and makes it competitive in some applications, e.g., enhancing short and medium-length LDPC codes to support longer length.
In the given paper we present a novel approach for constructing a QC-LDPC code of smaller length by lifting a given QC-LDPC code. The proposed method can be considered as a generalization of floor lifting. Also we prove several probabilistic statements concerning a theoretical improvement of the method with respect to the number of small cycles. Making some offline calculation of scale parameter it is possible to construct a sequence of QC-LDPC codes with different circulant sizes generated from a single exponent matrix using only floor and scale operations. The only parameter we store in memory is a constant needed for scaling.
A method to construct girth-12 (3,L) quasi-cyclic low-density parity-check (QC-LDPC) codes with all lengths larger than a certain given number is proposed, via a given girth-12 code subjected to some constraints. The lengths of these codes can be arbitrary integers of the form LP, provided that P is larger than a tight lower bound determined by the maximal element within the exponent matrix of the given girth-12 code. By applying the method to the case of row-weight six, we obtained a family of girth-12 (3,6) QC-LDPC codes for arbitrary lengths above 2688, which includes 30 member codes with shorter code lengths compared with the shortest girth-12 (3,6) QC-LDPC codes reported by O'Sullivan.
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.
The given paper presents a method for constructing a QC-LDPC code of shorter length by length adaption from a given QC-LDPC code of maximal length. The proposed method can be considered as a generalization of floor lifting. Making some offline calculation it is possible to construct a sequence of QC-LDPC codes with different circulant sizes generated from a single exponent matrix of QC-LDPC code which has the largest length. The only parameter stored in memory is a constant needed for scaling in the lifting procedure. Simulation results show that the proposed lifting method achieves around a 0.1 dB coding gain on short lengths over previous lifting approaches.