Magnetic recording devices are still competitive in the storage density race with solid-state devices thanks to new technologies such as two-dimensional magnetic recording (TDMR). Advanced data processing schemes are needed to guarantee reliability in TDMR. Data patterns where a bit is surrounded by complementary bits at the four positions with Manhattan distance $1$ on the TDMR grid are called plus isolation (PIS) patterns, and they are error-prone. Recently, we introduced lexicographically-ordered constrained (LOCO) codes, namely optimal plus LOCO (OP-LOCO) codes, that prevent these patterns from being written in a TDMR device. However, in the high-density regime or the low-energy regime, additional error-prone patterns emerge, specifically data patterns where a bit is surrounded by complementary bits at only three positions with Manhattan distance $1$, and we call them incomplete plus isolation (IPIS) patterns. In this paper, we present capacity-achieving codes that forbid both PIS and IPIS patterns in TDMR systems with wide read heads. We collectively call the PIS and IPIS patterns rotated T isolation (RTIS) patterns, and we call the new codes optimal T LOCO (OT-LOCO) codes. We analyze OT-LOCO codes and present their simple encoding-decoding rule that allows reconfigurability. We also present a novel bridging idea for these codes to further increase the rate. Our simulation results demonstrate that OT-LOCO codes are capable of eliminating media noise effects entirely at practical TD densities with high rates. To further preserve the storage capacity, we suggest using OP-LOCO codes early in the device lifetime, then employing the reconfiguration property to switch to OT-LOCO codes later. While the point of reconfiguration on the density/energy axis is decided manually at the moment, the next step is to use machine learning to take that decision based on the TDMR device status.

翻译：磁记录器件凭借二维磁记录（TDMR）等新技术，在存储密度竞争中仍与固态器件保持竞争力。为保证TDMR可靠性，需要先进的数据处理方案。在TDMR网格上，若某数据位被曼哈顿距离为1的四个互补位环绕，这种数据模式称为加型隔离（PIS）模式，该模式容易出错。近期我们引入了字典序约束（LOCO）码——最优加型LOCO（OP-LOCO）码，可防止这些模式写入TDMR器件。然而在高密度或低能量工况下，会出现其他易错模式：数据位仅被曼哈顿距离为1的三个互补位环绕，我们称之为不完全加型隔离（IPIS）模式。本文提出在采用宽读磁头的TDMR系统中同时禁止PIS和IPIS模式的容量可达码。我们将PIS和IPIS模式统称为旋转T隔离（RTIS）模式，新编码称为最优T型LOCO（OT-LOCO）码。我们分析了OT-LOCO码的特性，给出了支持可重构性的简单编解码规则，并提出了新颖的桥接方案以进一步提升码率。仿真结果表明，OT-LOCO码在实际TD密度下能以高码率完全消除介质噪声影响。为更好保存存储容量，建议在器件寿命初期使用OP-LOCO码，后期通过可重构特性切换至OT-LOCO码。目前密度/能量轴上的重构点由人工决定，下一步将基于TDMR器件状态通过机器学习实现自主决策。