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arXiv · 1004.1184

Circulant Arrays on Cyclic Subgroups of Finite Fields: Rank Analysis and Construction of Quasi-Cyclic LDPC Codes

Li Zhang·Shu Lin·Khaled Abdel-Ghaffar·Zhi Ding·Bo Zhou
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Abstract

This paper consists of three parts. The first part presents a large class of new binary quasi-cyclic (QC)-LDPC codes with girth of at least 6 whose parity-check matrices are constructed based on cyclic subgroups of finite fields. Experimental results show that the codes constructed perform well over the binary-input AWGN channel with iterative decoding using the sum-product algorithm (SPA). The second part analyzes the ranks of the parity-check matrices of codes constructed based on finite fields with characteristic of 2 and gives combinatorial expressions for these ranks. The third part identifies a subclass of constructed QC-LDPC codes that have large minimum distances. Decoding of codes in this subclass with the SPA converges very fast.

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Li Zhang, Shu Lin, Khaled Abdel-Ghaffar, Zhi Ding, Bo Zhou. 2010-04-07. Circulant Arrays on Cyclic Subgroups of Finite Fields: Rank Analysis and Construction of Quasi-Cyclic LDPC Codes. https://arxiv.org/abs/1004.1184

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