论文标题
受约束的de bruijn代码：属性，枚举，构造和应用程序
Constrained de Bruijn Codes: Properties, Enumeration, Constructions, and Applications
论文作者
论文摘要
de Bruijn图，其序列及其各种概括都在信息理论中发现了许多应用，其中包括过去十年中的许多新应用。在本文中，以新兴记忆技术的编码问题进行动机，定义了一组序列，这些序列概括了de bruijn图中的序列。这些序列也可以被定义并视为约束序列。因此，它们将被称为受约束的de bruijn序列，一组这样的序列将称为约束de bruijn代码。检查了此类代码的几种属性和替代定义，并将其分析为de Bruijn图（及其概括）和受约束序列中的广义序列。各种枚举技术用于计算任何给定的一组参数的序列总数。提出了从移位注册序列理论中的此类代码的构造方法。最后，我们展示了如何将这些受约束的de bruijn序列和代码应用于代码的构造中，以纠正$ \ ell $ -Symbol读取通道和赛道存储器通道中的同步错误。为此，这些代码在以前已知的代码上的规模上很出色。
The de Bruijn graph, its sequences, and their various generalizations, have found many applications in information theory, including many new ones in the last decade. In this paper, motivated by a coding problem for emerging memory technologies, a set of sequences which generalize sequences in the de Bruijn graph are defined. These sequences can be also defined and viewed as constrained sequences. Hence, they will be called constrained de Bruijn sequences and a set of such sequences will be called a constrained de Bruijn code. Several properties and alternative definitions for such codes are examined and they are analyzed as generalized sequences in the de Bruijn graph (and its generalization) and as constrained sequences. Various enumeration techniques are used to compute the total number of sequences for any given set of parameters. A construction method of such codes from the theory of shift-register sequences is proposed. Finally, we show how these constrained de Bruijn sequences and codes can be applied in constructions of codes for correcting synchronization errors in the $\ell$-symbol read channel and in the racetrack memory channel. For this purpose, these codes are superior in their size on previously known codes.
