On a simple method for detecting synchronization errors in coded messages

We investigate the problem of designing pairs ( ) of words with the property that, if each word of a coded message is prefixed by and suffixed by , the resulting set of coded messages is error detecting with finite delay. We consider (combinatorial) channels permitting any combination of the substitution, insertion, and deletion (SID) error types, and address the cases of both scattered and burst errors. A pair ( ) with the above property is evaluated in terms of three parameters: redundancy, delay of decoding, and frequency of the detectable errors. In the case of SID channels with burst errors, we provide a complete and explicit characterization of their error-detecting pairs ( ), which involves the period of the word .