Synchronization from insertions and deletions under a non-binary, non-uniform source

We study the problem of synchronizing two files X and Y at two distant nodes A and B that are connected through a two-way communication channel. We assume that file Y at node B is obtained from file X at node A by inserting and deleting a small fraction of symbols in X. More specifically, we consider the case where X is a non-binary non-uniform string, and deletions and insertions happen uniformly with rates β_d and β_i, respectively. We propose a synchronization protocol between node A and node B that needs to transmit O(q/H₂(β_d+β_i)n log 1/β_d+β_i) bits (where n is the length of X, q is the alphabet size and H₂ is the collision entropy of X) and reconstructs X at node B with error probability exponentially low in n. This protocol readily generalizes the recent result by Tabatabaei Yazdi and Dolecek that dealt with synchronization from binary uniform source and under only deletion errors.