Dependence of Capacity on Media Noise in Data Storage Systems

Abstract

The storage capacity of a medium, be it a one-dimensional wire, a two-dimensional platter, or a three-dimensional cube, ultimately depends on the intrinsic signal-to-noise ratio of the storage medium. The recording mechanism may be assumed to be error-free in the sense that any region of the medium, no matter how small, can be repeatedly and reliably set to one of two physically distinct states, 0 and 1. Also, the readout mechanism can be assumed to have unlimited resolution, in the sense that an arbitrarily small probe-tip can explore the storage medium and translate its local physical state into a real-valued binary signal of magnitude S0 or S1 in units of, say, volts. As far as the intrinsic storage capacity of the medium is concerned, the data-transfer rate and any time-dependent noise contributions to the readout signal can be made irrelevant. This is achieved by slowing down the readout process to allow integration over long intervals of time, thereby reducing the time-dependent component of noise to a negligibly small value. The only noise source that needs serious consideration, therefore, is the media noise, which manifests itself in the fluctuations of the readout signal observed when the probe-tip scans the medium, moving from one location to another to reveal the local state of the medium in its output signal, S0 or S1. The fundamental assumptions of this paper are: (i) the media noise is white, that is, its spatial distribution is uncorrelated; (ii) the power spectral density of the media noise is No volt2·cmd, where d is the dimensionality of the storage medium (d=1 for a wire, d=2 for a platter, d=3 for a cube). The storage capacity C of the medium per unit length, area, or volume (as the case may be) is found to be proportional to the medium's intrinsic signal-to-noise ratio in accordance with the formula C=0.059 (S1-S0)2/No in units of bits per cmd.