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Magnetic recording devices are still competitive in the storage density racethanks to new technologies such as two-dimensional magnetic recording (TDMR).Error-prone patterns where a bit is surrounded by complementary bits at thefour positions with Manhattan distance $1$ on the TDMR grid are called plusisolation (PIS) patterns. Recently, we introduced optimal plus LOCO (OP-LOCO)codes that prevent these patterns from being written. However, as the deviceages, error-prone patterns where a bit is surrounded by complementary bits atonly three positions with Manhattan distance $1$ emerge, and we call theseincomplete PIS (IPIS) patterns. In this paper, we present capacity-achievingcodes that forbid both PIS and IPIS patterns in TDMR systems with wide readheads. 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-LOCOcodes and derive their encoding-decoding rule. Simulation results demonstratethat OT-LOCO codes entirely eliminate media noise at practical TD densities. Wesuggest using OP-LOCO codes early in the device lifetime, then reconfiguring toOT-LOCO codes later on. Moreover, we introduce another coding scheme to removeRTIS patterns which offers lower complexity, lower error propagation, and trackseparation.

Eliminating Media Noise While Preserving Storage Capacity: Reconfigurable Constrained Codes for Two-Dimensional Magnetic Recording