The two-dimensional magnetic recording (TDMR) technology promises a remarkable increase in data storage density using the already-existing magnetic materials. Advanced TD signal processing techniques are required for this technology to fulfill its potential. Constrained coding, which prevents TD error-prone data patterns from being written, is among those techniques. In this paper, we propose lexicographically-ordered constrained (LOCO) coding schemes that offer low complexity, low latency, and low error propagation for TDMR systems with wide read heads, where coding can be applied on groups of 3 down tracks each. In particular, we introduce simple plus LOCO (SP-LOCO) and simple T LOCO (ST-LOCO) coding schemes, where codes defined over GF(2) and GF(4), respectively, are used instead of codes defined over GF (8), allowing the separation of uncoded streams. To better understand the behavior of the constrained-coded system, we derive the probability of transition, both in the horizontal and vertical directions, for the case of SP-LOCO and ST-LOCO coding, and we compare them to the case of optimal, rate-wise, LOCO codes. Moreover, we introduce simulation results on a practical TDMR model that demonstrate the performance gains achieved via the proposed schemes.

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). TDMR offers remarkable storage density increase without the need for new magnetic materials; however, advanced data processing schemes are needed to guarantee reliability. 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, with minimal redundancy that prevent these patterns from being written in a TDMR device. However, in the high-density regime or the low-energy regime (as the device ages), 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. Because of their shape, 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 derive 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 not only remarkably outperform OP-LOCO codes, but also entirely eliminate media noise effects, resulting from error-prone data patterns, at practical TD densities in the range [0.6,0.8) with high rates in the range [0.81,0.83]. At the TD density of 0.8, the OT-LOCO code of rate 0.8267 achieves a frame error rate (bit error rate) performance gain of about 1.15 orders (1.23 orders) of magnitude for all TDMR down (horizontal) tracks compared with the uncoded setting. To further preserve the storage capacity, we suggest using OP-LOCO codes, which have higher rates than OT-LOCO codes, early in the device lifetime, then employing the reconfiguration property to switch to OT-LOCO codes later in the device lifetime. 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 make that decision based on the TDMR device status. Moreover, we introduce another coding scheme to remove RTIS patterns in TDMR systems which offers lower complexity, lower error propagation, and track separation, at the expense of a limited rate loss.