Theoretical Bounds and Constructions of Codes in the Generalized Cayley Metric
Theoretical Bounds and Constructions of Codes in the Generalized Cayley Metric
复制标题
DOI：
10.1109/tit.2019.2899868
复制
发表时间：
2018-03
影响因子：
2.5
通讯作者：
Siyi Yang;Clayton Schoeny;L. Dolecek
中科院分区：
文献类型：
--
作者：
Siyi Yang;Clayton Schoeny;L. Dolecek
由于它们在各种应用中的潜力，包括云存储系统，基因组重新定制和闪光记忆，因此置换代码最近引起了巨大的研究兴趣。在本文中，我们研究了广义Cayley度量标准中置换代码的理论界限和构造。广义的Cayley度量标准捕获了置换中的广义换位误差的数量和先前研究的误差类型（包括换位和易位），而不会对转运段的长度和位置施加限制。基于Chee和Vu提出的所谓断点分析方法，我们首先提出一个导致订单最佳结构的编码框架，从而改善了不是订单优越的现有构造。然后，我们使用此框架还开发了一个订单最佳的编码方案，该方案是另外明确和系统的。
Permutation codes have recently garnered substantial research interest due to their potential in various applications, including cloud storage systems, genome resequencing, and flash memories. In this paper, we study the theoretical bounds and constructions of permutation codes in the generalized Cayley metric. The generalized Cayley metric captures the number of generalized transposition errors in a permutation and subsumes previously studied error types, including transpositions and translocations, without imposing restrictions on the lengths and positions of the translocated segments. Based on the so-called breakpoint analysis method proposed by Chee and Vu, we first present a coding framework that leads to order-optimal constructions, thus improving upon the existing constructions that are not order-optimal. We then use this framework to also develop an order-optimal coding scheme that is additionally explicit and systematic.