A combinatorial approach to finding the capacity of the discrete noiseless channel

Shannon defined the capacity of the discrete noiseless channel (DNC) and considered a finite-state model from which the capacity can be calculated. Alternatively, the DNC may be (and often is) represented by a finite list of forbidden strings. In this correspondence, we demonstrate the application of combinatorial techniques to finding the Shannon capacity of the DNC directly from the forbidden list. In our derivations, the case of noninteger symbol durations, as introduced by Csiszar, is considered.