Evaluation of Symmetric Mutual Information of the Simplified TDMR Channel Model

TL;DR

This paper introduces a simplified 2D TDMR channel model that captures key interference and noise effects, enabling analytical and numerical analysis of mutual information to inform data density limits.

Contribution

It proposes a simplified TDMR channel model with a closed-form Gaussian conditional PDF, facilitating mutual information approximation and analysis of TDMR system limits.

Findings

Mutual information depends on signal-dependent noise levels.

Low-rate coding improves data density in jitter-dominant regimes.

The model provides insights into the areal density limits of TDMR systems.

Abstract

In the present paper, a simplified two-dimensional magnetic recording (TDMR) channel model is proposed in order to capture the qualitative features of writing and read-back processes of TDMR systems.The proposed channel model incorporates the effects of both linear interference from adjacent bit-cells and signal-dependent noise due to irregular grain boundaries between adjacent bit-cells. The simplicity of the proposed model enables us to derive the closed form of the conditional PDF representing the probabilistic nature of the channel. The conditional PDF is Gaussian distributed and is parameterized by a signal-dependent covariance matrix. Based on this conditional PDF, a Monte Carlo method for approximating the symmetric mutual information of this channel is developed. The symmetric mutual information is closely related to the areal density limit for TDMR systems. The numerical results suggest that we may need low-rate coding, e.g., 2/3 or 1/2, when the jitter-like noise becomes dominant.