LDPC Codes Based on the Space of Symmetric Matrices over Finite Fields
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, $\cal{C}(n,q)$...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
23.05.2016
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Subjects | |
Online Access | Get full text |
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Summary: | 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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DOI: | 10.48550/arxiv.1605.07273 |