Coding with Noiseless Feedback over the Z-channel

In this paper, we consider encoding strategies for the Z-channel with noiseless feedback. We analyze combinatorial setting where maximum number of errors inflicted by an adversary is proportional to transmissions, which goes infinity. Without feedback, it known that rate optimal asymmetric-error-correcting codes error fraction $\tau \ge 1/4$ vanishes as blocklength grows. give efficient feedback scheme notation="LaTeX">$n$ transmissions achieves a positive any < 1$ and notation="LaTeX">$n\to \infty $ . Additionally, state upper bound on asymptotically long asymmetric error-correcting codes.