Complete j-MDP Convolutional Codes
Complete j-MDP Convolutional Codes
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DOI：
10.1109/tit.2020.3015698
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发表时间：
2020-12-01
影响因子：
2.5
通讯作者：
Lieb, Julia
中科院分区：
文献类型：
--
作者：
Almeida, Paulo J.;Lieb, Julia
最大距离轮廓（MDP）卷积码已被证明是非常适合在擦除信道上传输。此外，完整MDP卷积码的子类能够在出现一系列擦除后重新开始解码。然而，在小尺寸的字段上缺乏这些代码的构造。在这篇文章中，我们介绍了完全j-MDP卷积码的概念，它是完全MDP卷积码的推广，并描述了它们的解码特性。特别是，我们提出了一个解码算法，在给定的时间延迟T内的解码擦除，并表明，完整的T-MDP卷积码是最佳的这种算法。此外，利用MAPLE软件进行计算机搜索，确定了（2，1，2）完全j-MDP卷积码存在的最小二元和非二元域长度，并给出了相应的构造方法.本文给出了在最小可能域F-13和F-16上的所有（2，1，2）完全MDP卷积码的描述，并通过随机计算机搜索给出了F-128上的（2，1，3）完全4-MDP卷积码的构造.
Maximum distance profile (MDP) convolutional codes have been proven to be very suitable for transmission over an erasure channel. In addition, the subclass of complete MDP convolutional codes has the ability to restart decoding after a burst of erasures. However, there is a lack of constructions of these codes over fields of small size. In this article, we introduce the notion of complete j-MDP convolutional codes, which are a generalization of complete MDP convolutional codes, and describe their decoding properties. In particular, we present a decoding algorithm for decoding erasures within a given time delay T and show that complete T-MDP convolutional codes are optimal for this algorithm. Moreover, using a computer search with the MAPLE software, we determine the minimal binary and non-binary field size for the existence of (2, 1, 2) complete j-MDP convolutional codes and provide corresponding constructions. We give a description of all (2, 1, 2) complete MDP convolutional codes over the smallest possible fields, namely F-13 and F-16 and we also give constructions for (2, 1, 3) complete 4-MDP convolutional codes over F-128 obtained by a randomized computer search.