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International Conference on Wireless Communications and Signal Processing (WCSP)

Construction of Finite Field Based QC-LDPC Codes from Isomorphism Perspective

Huaan Li, Hengzhou Xu, Baoming Bai, Min Zhu, Ji Zhang

Published Oct 1, 2019• 1 citation
Publisher

Abstract

There are many algebraic tools, e.g., finite fields and combinatorial designs, for constructing good quasi-cyclic LDPC (QC-LDPC) codes. In particular, QC-LDPC codes designed based on two arbitrary subsets of a given finite field perform very well and some well-known algebraic constructions of QC-LDPC codes have been verified as special cases of this method. How to choose these two subsets to further improve the performance of finite field based QC-LDPC codes is of interest. In this paper, we study such codes and analyze their structural properties from isomorphism perspective, and generalize some rules to efficiently determine the non-isomorphic finite field based codes. By comparing the cycle distributions of non-isomorphic codes, we can easily construct the finite field based QC-LDPC codes with larger girth and fewer short cycles. These codes generally perform very well and can be used as the ingredients of some further processings, e.g., masking. Numerical results show that the constructed codes have better performance with the iterative decoding algorithms.

DOI
10.1109/wcsp.2019.8927973

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This paper presents a simple and very flexible method for constructing quasi-cyclic (QC) low density paritycheck (LDPC) codes based on finite fields. The code construction is based on two arbitrary subsets of elements from a given field. Some well known constructions of QC-LDPC codes based on finite fields and combinatorial designs are special cases of the proposed construction. The proposed construction in conjunction with a technique, known as masking, results in codes whose Tanner graphs have girth 8 or larger. Experimental results show that codes constructed using the proposed construction perform well and have low error-floors. Also presented in the paper is a reduced-complexity iterative decoding scheme for QC-LDPC codes based on the section-wise cyclic structure of their parity-check matrices. The proposed decoding scheme is an improvement of an earlier proposed reduced-complexity iterative decoding scheme.
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Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes require less hardware resources due to the quasi-cyclic structure of parity-check matrices.In this paper, two improved methods for constructing QC-LDPC codes are proposed.Firstly, in order to make sure the masked LDPC codes have flexible code rate and code length, an improved construction of masking matrix is presented.The proposed regular masking matrix of QC-LDPC codes have the girth at least 6.Then, the irregular codes are constructed by using improved finite field approach and PEG algorithm, which result in large girth and less short cycles.Simulations demonstrate that the proposed QC-LDPC codes have both lower error floor and good waterfall performance.
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