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arXiv · 1605.07273

LDPC Codes Based on the Space of Symmetric Matrices over Finite Fields

Meng Zhao·Changli Ma·Qi Wang
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Abstract

In this paper, we present a new method for explicitly constructing regular low-density parity-check (LDPC) codes based on $\mathbb{S}_{n}(\mathbb{F}_{q})$, the space of $n\times n$ symmetric matrices over $\mathbb{F}_{q}$. Using this method, we obtain two classes of binary LDPC codes, $\cal{C}(n,q)$ and $\cal{C}^{T}(n,q)$, both of which have grith $8$. Then both the minimum distance and the stopping distance of each class are investigated. It is shown that the minimum distance and the stopping distance of $\cal{C}^{T}(n,q)$ are both $2q$. As for $\cal{C}(n,q)$, we determine the minimum distance and the stopping distance for some special cases and obtain the lower bounds for other cases.

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BibTeXRIS

Meng Zhao, Changli Ma, Qi Wang. 2016-05-25. LDPC Codes Based on the Space of Symmetric Matrices over Finite Fields. https://arxiv.org/abs/1605.07273

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