论文标题
模式的秘密算术：一种基于词典索引设计约束代码的一般方法
The Secret Arithmetic of Patterns: A General Method for Designing Constrained Codes Based on Lexicographic Indexing
论文作者
论文摘要
受限的代码用于防止在各种数据存储和数据传输系统中发生错误。它们可以帮助提高磁性存储设备的存储密度，管理电子存储设备的寿命以及提高电线传输的可靠性。我们最近引入了词典有序约束（LOCO）代码的家族。这些代码通过简单的编码和解码实现容量，并且易于重新配置。在本文中，我们通过提出一种系统的方法来概括我们的工作，该方法指导代码设计人员一旦已知有限的数据模式集，可以根据词典索引构建任何受约束的代码。特别是，我们将禁忌模式的集合直接连接到代码的基础性以及发现与代码字相关的索引的规则。通过这样做，我们揭示了模式的秘密算术，并使代码设计变得更加容易。我们为新的二维磁记录（TDMR）技术设计了最佳（速率）约束代码。由于仅应用新代码，我们显示出显着的性能提高。此外，我们展示了如何设计和用于进一步降低复杂性的近乎最佳约束代码。
Constrained codes are used to prevent errors from occurring in various data storage and data transmission systems. They can help in increasing the storage density of magnetic storage devices, in managing the lifetime of electronic storage devices, and in increasing the reliability of data transmission over wires. We recently introduced families of lexicographically-ordered constrained (LOCO) codes. These codes achieve capacity with simple encoding and decoding, and they are easy to reconfigure. In this paper, we generalize our work on LOCO codes by presenting a systematic method that guides the code designer to build any constrained code based on lexicographic indexing once the finite set of data patterns to forbid is known. In particular, we connect the set of forbidden patterns directly to the cardinality of the code and to the rule that uncovers the index associated with a codeword. By doing that, we reveal the secret arithmetic of patterns, and make the code design significantly easier. We design optimal (rate-wise) constrained codes for the new two-dimensional magnetic recording (TDMR) technology. We show notable performance gains as a result of solely applying the new codes. Moreover, we show how near-optimal constrained codes be designed and used to further reduce complexity.
