On the capabilities of codes to correct synchronization errors

A synchronization error is said to occur when either a bit which does not belong appears, or is detected in a channel between bits which were transmitted; or a bit which was transmitted is lost or not detected. A model for such a channel will be proposed, and a lower and upper bound on the redundancy necessary to correct a given error rate will be derived. We will consider the case of single synchronization error correction in detail, and stronger bounds will be derived for that case. We will consider multiple adjacent synchronization errors as a special case, and show that the bounds can be tightened in this case as well.