Finite-state modulation codes for data storage

Abstract

The authors provide a self-contained exposition of modulation code design methods based upon the state splitting algorithm. They review the necessary background on finite state transition diagrams, constrained systems, and Shannon (1948) capacity. The state splitting algorithm for constructing finite state encoders is presented and summarized in a step-by-step fashion. These encoders automatically have state-dependent decoders. It is shown that for the class of finite-type constrained systems, the encoders constructed can be made to have sliding-block decoders. The authors consider practical techniques for reducing the number of encoder states as well as the size of the sliding-block decoder window. They discuss the class of almost-finite-type systems and state the general results which yield noncatastrophic encoders. The techniques are applied to the design of several codes of interest in digital data recording.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>