论文标题
加权芦苇 - 固体卷积代码
Weighted Reed-Solomon convolutional codes
论文作者
论文摘要
在本文中，我们提出了一种新型卷积代码的具体代数结构。这些代码建立在广义的Vandermonde矩阵上，因此可以将其视为将芦苇 - 固体块代码的自然扩展到卷积代码的背景。因此，我们称它们为加权的芦苇 - 溶剂（WRS）卷积代码。我们表明，在对定义参数的某些约束下，这些代码是最大距离轮廓（MDP），这意味着它们在列距离轮廓中具有最大可能的增长。我们研究获得MDP的WRS卷积代码所需的领域大小，并将其与文献中MDP卷积代码的现有常规结构进行比较，这表明在许多情况下，WRS卷积代码需要明显较小的字段。
In this paper we present a concrete algebraic construction of a novel class of convolutional codes. These codes are built upon generalized Vandermonde matrices and therefore can be seen as a natural extension of Reed-Solomon block codes to the context of convolutional codes. For this reason we call them weighted Reed-Solomon (WRS) convolutional codes. We show that under some constraints on the defining parameters these codes are Maximum Distance Profile (MDP), which means that they have the maximal possible growth in their column distance profile. We study the size of the field needed to obtain WRS convolutional codes which are MDP and compare it with the existing general constructions of MDP convolutional codes in the literature, showing that in many cases WRS convolutional codes require significantly smaller fields.
