On the capacity of the bit-shift magnetic recording channel

Summary form only given. The bit-shift (peak-shift) effect is often encountered in magnetic recording, and it arises mainly owing to the effect of noise and readout impairments and clock jittering. The authors have investigated the degrading effect of this phenomenon on the capacity of a binary (d, k) coded system, commonly used in magnetic recording. The bit-shift channel is best formulated in terms of phrase lengths. A phrase starts with none, one, or more zeros and terminates with a single one; thus any binary {0, 1} sequence is uniquely decomposable into a concatenated sequence of phrases. The shift effect, restricted here to no more than a single channel bit position, either shrinks the input phrase length or expands it by 1. The authors have restricted the discussion to d ≥ 2; thus neither additional phrases are generated nor existing phrases destroyed. An increasingly tight and easily calculable sequence of upper and lower bounds on capacity (normalized per channel bit input) has been derived. The capacity of a concatenated scheme in which the bit-shift channel is followed by a binary symmetric channel has also been addressed, and certain upper and lower bounds have been obtained.