Synchronization of a class of codes derived from cyclic codes

This paper presents a new class of synchronizable error-correcting codes which are derivable from cyclic codes by restraining some of their information symbols. They are called subset codes because each code constitutes a subset of code words in the parent cyclic code. The ability of the subset codes to detect and correct loss of synchronism, or slip, in both noiseless and noisy channels is examined. In particular, given a t-error-correcting cyclic code, there exists a subset code that can correct any combination of slip and additive error whose total magnitude does not exceed t. Moreover, when the received word is in synchronism, the decoder automatically corrects any additive error pattern the parent cyclic code could correct. For channels in which slip is small and occurs infrequently, the subset codes appear to be the most efficient available. In other situations they are generally efficient and in addition their decoding procedures are straightforward.The manner in which the information symbols are restrained is the same as for the extended cyclic codes of Bose and Caldwell [1], and Weldon [2]. However, unlike the extended cyclic codes which have redundant symbols added to both ends of each code word, the block length of the subset codes is the same as the parent cyclic codes