Synchronization of cyclic codes in the presence of burst errors

This paper deals with the ability of coset codes derivable from (n, k) cyclic codes to detect and correct loss of synchronization, or slip, in a burst-error channel. Results are presented both for general cyclic codes and burst error correcting cyclic codes. In particular, the Fire codes, which correct single burst errors, are considered. Two classes of burst-error channels are considered, namely, Type I and Type II. In Type I channels, slip and additive burst errors cannot occur simultaneously in any received n-tuple. In the more general Type II channels, this restriction is removed. It is shown that certain coset codes can correct slip and burst errors even when they occur simultaneously. Furthermore, both the magnitude and the direction of the slip can be determined by examining the syndrome of the received n-tuple