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IEEE East-West Design & Test Symposium (EWDTS)

Generalization of floor lifting for QC-LDPC codes

Vasiliy S. Usatyuk, Егоров Сергей Иванович

Published Sep 1, 2017• 1 citation
Publisher

Abstract

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.

DOI
10.1109/ewdts.2017.8110069

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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.
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.
The given paper presents several probabilistic statements for the methods related to constructing a QC-LDPC code of shorter length by length adaption from a given QC-LDPC code of maximal length. Several probabilistic statements concerning a theoretical improvement of the generalization of floor lifting method with respect to the number of small cycles are proved. Simulation results show that the generalization of floor lifting method under base graph 2 (BG2) allow to achieves from 0.1 to 0.3 dB coding gain.
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
In this paper, we analyze some cycle properties of quasi-cyclic low-density parity-check (QC-LDPC) codes and show that the girth of a QC-LDPC code is upper bounded by a certain number introduced by the structure of its mother matrix. We also propose a simple method to extend QC-LDPC codes of large length by lifting QC-LDPC codes of smaller length. In particular, it is possible to generate them from a single exponent matrix by a proper modulo-operation. Simulation results show that the more we apply the lifting to QC-LDPC codes, the more memory efficiency becomes better, but it may induce a little performance degradation
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.
Quasi-cyclic low-density parity-check (QC-LDPC) codes based on protographs are of great interest to code designers because analysis and implementation are facilitated by the protograph structure and the use of circulant permutation matrices for protograph lifting. However, these restrictions impose undesirable fixed upper limits on important code parameters, such as minimum distance and girth. In this paper, we consider an approach to constructing QC-LDPC codes that uses a two-step lifting procedure based on a protograph, and, by following this method instead of the usual one-step procedure, we obtain improved minimum distance and girth properties. We also present two new design rules for constructing good QC-LDPC codes using this two-step lifting procedure, and in each case we obtain a significant increase in minimum distance and achieve a certain guaranteed girth compared to one-step circulant-based liftings. The expected performance improvement is verified by simulation results.