Bounds on the capacity of the peak shift magnetic recording channel

A simple statistical channel model is suggested to account for single-position peak (bit) shifts, which were identified to be one of the major impairments in magnetic recording. Simple lower and upper bounds on the capacity of this channel with (d,k) channel inputs (commonly used in magnetic recording) are presented. For d⩾2, this channel is conveniently described in terms of phrase lengths where a bit shift causes a phrase either to shrink or to expand. The inherent correlation present in consecutive shift affected phrases manifests itself in memory introduced into the channel model. The lower bound, when evaluated for a certain phrase distribution, is also a lower bound on the zero error capacity for this channel