Feedback Insertion-Deletion Codes

In this paper, a new problem of transmitting information over the adversarial insertion-deletion channel with feedback is introduced. Suppose that encoder transmits $n$ binary symbols one-by-one channel, in which some can be deleted and additional inserted. After each transmission, notified about insertions or deletions have occurred within previous transmission encoding strategy adapted accordingly. The goal to design an able transmit error-free as much possible under assumption total number limited by $\tau n$, $0<\tau<1$. We show how reduced messages substitution channel. Thereby, maximal asymptotic rate codes completely established. for has been partially determined Berlekamp later finished Zigangirov. However, analysis lower bound Zigangirov quite complicated. revisit Zigangirov's result present more elaborate version his proof.