Relationships between different error-correcting capabilities of a code

SID channels are discrete channels represented by expressions that involve combinations of the error types substitution, insertion, and deletion. Based on the SID channel model, a simple distance is defined that generalizes the Hamming and Levenshtein distances. For a certain class of SID channels, the distance is used to obtain a unifying necessary and sufficient condition for the error correcting capability that corresponds to the channel in question. Moreover, it is shown that for many SID channels whose expressions include the insertion type their error-correcting codes coincide with those for SID channels whose expressions result by removing the insertion type or by replacing it with the deletion type.