Magnetic recording devices are still competitive in the storage density race thanks to new technologies such as two-dimensional magnetic recording (TDMR). Error-prone 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. Recently, we introduced optimal plus LOCO (OP-LOCO) codes that prevent these patterns from being written. However, as the device ages, error-prone patterns where a bit is surrounded by complementary bits at only three positions with Manhattan distance $1$ emerge, and we call these incomplete PIS (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 these patterns rotated T isolation (RTIS) patterns, and we call the new codes optimal T LOCO (OT-LOCO) codes. We analyze OT-LOCO codes and derive their encoding-decoding rule. Simulation results demonstrate that OT-LOCO codes entirely eliminate media noise at practical TD densities. We suggest using OP-LOCO codes early in the device lifetime, then reconfiguring to OT-LOCO codes later on. Moreover, we introduce another coding scheme to remove RTIS patterns which offers lower complexity, lower error propagation, and track separation.

翻译：磁记录设备凭借二维磁记录等新技术在存储密度竞争中仍具优势。在TDMR网格上，对于曼哈顿距离为1的四个位置，被互补比特包围的比特所形成的易错模式称为加孤立（PIS）模式。近期，我们提出了防止这些模式被写入的最优加LOCO（OP-LOCO）码。然而随着设备老化，仅在曼哈顿距离为1的三个位置被互补比特包围的易错模式（即不完整加孤立模式，简称IPIS模式）开始出现。本文针对采用宽读磁头的TDMR系统，提出了禁止PIS和IPIS两种模式的容量可达码。我们将这些模式统称为旋转T隔离（RTIS）模式，并将新码称为最优T LOCO（OT-LOCO）码。我们分析了OT-LOCO码并推导了其编解码规则。仿真结果表明，在实用TD密度下，OT-LOCO码可完全消除介质噪声。我们建议在设备寿命前期使用OP-LOCO码，后期再重构为OT-LOCO码。此外，我们还提出了一种去除RTIS模式的替代编码方案，该方案具有更低复杂度、更低错误传播及磁道分离特性。