Achievable Rates over Insertion Channels

We consider achievable rates over binary input insertion channels for small values of insertion probabilities by computing bounds on the mutual information rate of insertion channels for independent uniformly distributed (i.u.d.) input sequences. We consider two scenarios: random insertions, where transmitted bits are replaced with a certain probability by two random bits independent of any other insertions, and sticky channels where bits are duplicated with a certain probability again independent of the other insertion errors. Derived lower bounds improve the existing results available in the literature as demonstrated by specific examples.