  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.
