Non-Binary Constrained Codes for Two-Dimensional Magnetic Recording

TL;DR

This paper introduces non-binary constrained codes for two-dimensional magnetic recording that prevent isolation patterns, improving reliability with minimal redundancy and complexity, leveraging the specific operation of read heads collecting signals from three tracks.

Contribution

The paper designs capacity-achieving non-binary constrained codes tailored for 2D magnetic recording, reducing redundancy and complexity while preventing specific interference patterns.

Findings

Codes achieve capacity with less than 3% redundancy.

Designed codes prevent 3x3 isolation patterns effectively.

Method exploits the operation of three-track read heads.

Abstract

The two-dimensional magnetic recording (TDMR) technology promises storage densities of $10$ terabits per square inch. However, when tracks are squeezed together, a bit stored in the two-dimensional (TD) grid suffers inter-symbol interference (ISI) from adjacent bits in the same track, and inter-track interference (ITI) from nearby bits in the adjacent tracks. A bit is highly likely to be read incorrectly if it is isolated in the middle of a $3 \times3$ square; surrounded by its complements, horizontally and vertically. We improve the reliability of TDMR systems by designing two-dimensional constrained codes that prevent these square isolation patterns. We exploit the way TD read heads operate to design our codes, and we focus on TD read heads that collect signals from three adjacent tracks. We represent the two-dimensional square isolation constraint as a one-dimensional constraint on an alphabet of eight non-binary symbols. We use this new representation to construct a non-binary lexicographically-ordered constrained code where one third of the information bits are unconstrained. Our TD constraint codes are capacity-achieving, and the data protection is achieved with redundancy less than $3\%$ and at modest complexity.