Coding for High-Density Recording on a 1-D Granular Magnetic Medium

TL;DR

This paper models and analyzes error-correcting codes and channel capacity for high-density 1-D magnetic storage where errors depend on neighboring bits, providing bounds on code size and channel capacity.

Contribution

It introduces a combinatorial error model for magnetic storage and derives bounds on code cardinality and channel capacity, advancing understanding of data reliability in high-density media.

Findings

Bounds on code cardinality for the error model

Lower and upper bounds on channel capacity

Capacity estimates using symmetric capacity and stochastic degradation

Abstract

In terabit-density magnetic recording, several bits of data can be replaced by the values of their neighbors in the storage medium. As a result, errors in the medium are dependent on each other and also on the data written. We consider a simple one-dimensional combinatorial model of this medium. In our model, we assume a setting where binary data is sequentially written on the medium and a bit can erroneously change to the immediately preceding value. We derive several properties of codes that correct this type of errors, focusing on bounds on their cardinality. We also define a probabilistic finite-state channel model of the storage medium, and derive lower and upper estimates of its capacity. A lower bound is derived by evaluating the symmetric capacity of the channel, i.e., the maximum transmission rate under the assumption of the uniform input distribution of the channel. An upper bound is found by showing that the original channel is a stochastic degradation of another, related channel model whose capacity we can compute explicitly.