Bounds on the Capacity of Channels with Insertions, Deletions and Substitutions

We present novel bounds on the capacity of binary channels with independent and identically distributed insertions, deletions, and substitutions. The proposed bounds are obtained by exploiting an auxiliary system where the channel is the same as the one in the system of interest, but the receiver is provided with (partial) genie-aided information on the insertion/deletion process. In particular, we show that, when this information is revealed, we obtain a memoryless channel whose capacity, evaluated by means of the Blahut-Arimoto algorithm, gives an upper bound on the capacity of interest. We also show that capacity lower bounds can be derived as well, by exploiting the same auxiliary system and resorting to suitable information-theoretical inequalities. In most scenarios, the proposed bounds improve the existing ones, and significantly narrow the region to which the actual capacity can belong.