Minimal self-correcting shift counters

Abstract

In some applications of shift counters, self initialization is an advantage. It eliminates the need for complex initialization and guarantees the return to the original state sequence after a temporary failure. The low operating frequencies and large areas of the available self correcting shift counters, however, impose severe limitations to their use. This poor performance is partially due to a widely used design method. It consists of modifying the state diagram of a counter with the desired modulus until a single cycle is left. Due to the additional hardware required to change state transitions, the final circuit tends to be slow and large. The paper presents a technique for determining self correcting shift counters by selecting the feedback functions from a large set of functions. The set is searched for functions satisfying a minimization criterion. Self correcting shift counters with up to 10 stages have been determined. These counters are faster and smaller than the self correcting shift counters available from the literature. A table of self correcting shift counters with 6 stages is included in the paper.