Analytical Lower Bounds on the Capacity of Deletion Channels

We develop several analytical lower bounds on the capacity of deletion channels by considering independent uniformly distributed (i.u.d.) inputs and computing lower bounds on the mutual information rate between the input and output sequences. We consider the usual independent identically distributed (i.i.d.) binary deletion channel, i.i.d. deletion/substitution channel and i.i.d. deletion channel with additive white Gaussian noise (AWGN). We emphasize the importance of these results by noting that 1) our results are the first analytical bounds on the capacity of deletion-AWGN channels, 2) the results developed are the best available analytical lower bounds on the deletion/substitution case, 3) for the deletion only channel, our results compete well with the best available lower bounds for small deletion probabilities and they explicitly obtain the first order terms in the recently derived capacity expansions.