Improved capacity lower bounds for channels with deletions and insertions

New lower bounds are obtained for the capacity of a binary channel with deletions and insertions. Each input bit to the channel is deleted with probability d, or an extra bit is inserted after it with probability i, or it is transmitted unmodified with probability 1-d-i. This paper builds on the idea introduced in [1] of using a sub-optimal decoder that decodes the positions of the deleted and inserted runs, in addition to the transmitted codeword. The mutual information between the channel input and output sequences is expressed as the sum of the rate achieved by this decoder and the rate loss due to its sub-optimality. The main contribution is an analytical lower bound for the rate loss term which leads to an improvement in the capacity lower bound of [1]. For the special case of the deletion channel, the new bound is larger than the previous best lower bound for deletion probabilities up to 0.3.