On the capacity of channels with synchronization errors

Abstract—We consider a new formulation of a class of syn-chronization error channels and derive analytical bounds and numerical estimates for the capacity of these channels. For the binary channel with only deletions, we obtain an expression for the symmetric information rate in terms of subsequence weights which reduces to a tight lower bound for small deletion proba-bilities. We are also able to exactly characterize the Markov-1 rate for the binary channel with only replications. For a channel that introduces deletions as well as replications of input symbols, we design two sequences of approximating channels with favourable properties. In particular, we parameterize the state space associated with these approximating channels and show that the information rates approach that of the deletion-replication channel as the state space grows. For the case of the channel where deletions and replications occur with the same probabilities, a stronger result in the convergence of mutual information rates is shown. The numerous advantages this new formulation presents are explored. Index Terms—Synchronization errors, deletions, insertions, replications, channel capacity. I