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. In this correspondence, 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 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 replacing the insertion type with the deletion type.