论文标题
QC-LDPC代码来自差矩阵和覆盖阵列的差异
QC-LDPC Codes from Difference Matrices and Difference Covering Arrays
论文作者
论文摘要
我们提供了一个框架，用于概括使用横向设计或相关结构（例如相互正交拉丁正方形）的构建框架。我们的构造提供了更广泛的代码长度和代码速率。类似的早期构造依赖于有限阶的有限域的存在。相比之下，此处构建的LDPC代码基于差异矩阵和覆盖阵列的差异，可用于任何订单$ a $的结构。他们满足RC约束，并具有$ a $奇数，长度$ a^2 $和$ $ 1- \ frac {4a-3} {a^2} $，以及$ a $ a $偶数，长度$ a^2-a $，并至少$ 1- \ frac {4a-6} {4a-6} {a^2-a} {a^2-a} $。当$ 3 $不划分$ a $时，这些LDPC代码的距离至少为$ 8 $。当$ a $是奇怪的，$ 3 $和$ 5 $都不分配$ a $时，我们的建筑提供了一个无限的QC-LDPC代码家族，最小距离至少$ 10 $。构造的简单性使我们能够从理论上验证这些属性，并在分析中确定最小距离和停止代码的距离。我们在AWGN（通过仿真）上的代码的BER和FER性能至少等同于先前构建的代码，而在某些情况下则大大优于它们。
We give a framework for generalizing LDPC code constructions that use Transversal Designs or related structures such as mutually orthogonal Latin squares. Our construction offers a broader range of code lengths and codes rates. Similar earlier constructions rely on the existence of finite fields of order a power of a prime. In contrast the LDPC codes constructed here are based on difference matrices and difference covering arrays, structures available for any order $a$. They satisfy the RC constraint and have, for $a$ odd, length $a^2$ and rate $1-\frac{4a-3}{a^2}$, and for $a$ even, length $a^2-a$ and rate at least $1-\frac{4a-6}{a^2-a}$. When $3$ does not divide $a$, these LDPC codes have stopping distance at least $8$. When $a$ is odd and both $3$ and $5$ do not divide $a$, our construction delivers an infinite family of QC-LDPC codes with minimum distance at least $10$. The simplicity of the construction allows us to theoretically verify these properties and analytically determine lower bounds for the minimum distance and stopping distance of the code. The BER and FER performance of our codes over AWGN (via simulation) is at the least equivalent to codes constructed previously, while in some cases significantly outperforming them.
