Bounds on the Capacity of a Channel with Bit Shift

A simple statistical channel model is suggested to account for single position bit shifts that have been identified as one of the major impairments in magnetic recording. The authors investigate bounds on the capacity of this channel where the channel inputs are the (d,k) codes commonly used in magnetic recordings. For d>or=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 introduces memory into the channel model. Sequences of nondecreasing lower bounds and nonincreasing upper bounds on the capacity are evaluated and investigated for a variety of parameters. Lower bounds on the zero-error capacity are also studied. The channel model is extended to a concatenated scheme of a bit shift channel connected in tandem with the binary symmetric channel, thus capturing both major error generating mechanisms-the bit shifts as well as randomly generated errors. Lower and upper bounds on the capacity of this concatenated channel model with (d,k) input sequences are derived and discussed.