On Transmission Over Deletion Channels

In this paper, we develop lower bounds on the achievable rate for deletion channels. Deletion channels occur when symbols are randomly dropped, and a subsequence o f th transmitted symbols is received. In deletion channels, unlike erasure channels, there is no s ide-information about which subsequence is received. We show that the achievable rate in deletion chann els differs from that of erasure channels by at mostH0(pd) pd log K K 1 bits, wherepd is the deletion probability, K is the alphabet size and H0( ) is the binary entropy function. We also develop lower bounds for the binary deletion channel that improve the bounds reported in the literature.