The two-dimensional magnetic recording (TDMR) technology promises storage densities of 10 Tbits/in2. However, when tracks are squeezed together, a bit stored in the two-dimensional (TD) grid suffers inter-symbol interference (ISI) from adjacent bits in the same track and inter-track interference (ITI) from nearby bits in the adjacent tracks. A bit is highly likely to be read incorrectly if it is isolated in the middle of a $3 \times 3$ square, surrounded by its complements, horizontally and vertically. We improve the reliability of TDMR systems by designing TD constrained codes that prevent these square isolation patterns. We exploit the way TD read heads operate to design our codes, and we focus on TD read heads that collect signals from three adjacent tracks. We represent the two-dimensional square isolation constraint as a one-dimensional constraint on an alphabet of eight non-binary symbols. We use this new representation to construct a non-binary lexicographically-ordered constrained code where one third of the input information bits are unconstrained. Our TD constraint codes are capacity-achieving, and the data protection is achieved with redundancy less than 3% and at modest complexity.

中文翻译：

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二维磁记录的非二进制约束码

二维磁记录 (TDMR) 技术有望实现 10 Tbits/in2 的存储密度。然而，当轨道被挤压在一起时，存储在二维 (TD) 网格中的位会受到来自同一轨道中相邻位的符号间干扰 (ISI) 和来自相邻轨道中相邻位的轨道间干扰 (ITI) . 如果某个位被隔离在 $3 \times 3$ 正方形的中间，并被其补码水平和垂直地包围，那么它很可能被错误地读取。我们通过设计防止这些方形隔离模式的 TD 约束代码来提高 TDMR 系统的可靠性。我们利用 TD 读头的操作方式来设计我们的代码，我们专注于从三个相邻磁道收集信号的 TD 读头。我们将二维方形隔离约束表示为八个非二进制符号字母表上的一维约束。我们使用这种新的表示来构造一个非二进制的字典序约束代码，其中三分之一的输入信息位是不受约束的。我们的 TD 约束代码是容量实现的，并且以低于 3% 的冗余和适度的复杂性实现了数据保护。