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

翻译：在本文中, 我们考虑 Z 通道的编码策略, 使用无噪音反馈。 我们分析一个对手造成的最大错误数量与传输数量成正比的组合设置, 该组合设置与传输数量成无穷无穷。 没有反馈, 已知错误分数 $\ tau\ ge 1/4 美元的最佳不对称- eror- 校正代码率随整段长度增长而消失。 在本文中, 我们给出一个有效的反馈编码方案, 以 $n 的传输实现任何部分错误的正率 $\ tau < 1$ 和 $n\ t\ infty$ 。 此外, 我们声明了非随机长反馈非对称错误校正率的上限 。