Novel bounds on the capacity of binary channels with deletions and substitutions

We present novel bounds on the capacity of binary channels with independent and identically distributed deletions and substitutions. The proposed bounds are obtained by exploiting an auxiliary system where the channel is the same as in the system of interest, but the receiver is provided with (partial) genie-aided information on the deletion/substitution process. In the case of the deletion channel, that is, when no substitutions occur, the proposed upper bound improves the existing ones for most values of the deletion probability, while the proposed lower bound does not. On the other hand, when the channel model also includes substitution errors, both proposed bounds improve the existing ones, significantly narrowing the region to which the actual capacity can belong.