论文标题
反馈插入删除代码
Feedback Insertion-Deletion Codes
论文作者
论文摘要
在本文中,引入了一个新的问题,即通过反馈通过反向插入渠道传输信息。假设编码器在通道上一对一地传输$ n $二进制符号,其中可以删除某些符号,并且可以插入一些其他符号。每次传输后,都会通知编码器,以了解先前传输中发生的插入或删除,并且可以相应地调整编码策略。目的是设计一个能够在删除总数和插入的假设限制为$τn$,$ 0 <τ<1 $的情况下,能够传输尽可能多的信息的编码器。我们展示了如何将这个问题简化为通过替换通道传输消息的问题。因此,完全确定了反馈插入码代码的最大渐近率。对抗替代通道的最大渐近率已由Berlekamp部分确定,后来由Zigangirov完成。但是,Zigangirov对下限的分析非常复杂。我们重新审视了Zigangirov的结果,并提供了他的证明的更精致版本。
In this paper, a new problem of transmitting information over the adversarial insertion-deletion channel with feedback is introduced. Suppose that the encoder transmits $n$ binary symbols one-by-one over a channel, in which some symbols can be deleted and some additional symbols can be inserted. After each transmission, the encoder is notified about the insertions or deletions that have occurred within the previous transmission and the encoding strategy can be adapted accordingly. The goal is to design an encoder that is able to transmit error-free as much information as possible under the assumption that the total number of deletions and insertions is limited by $τn$, $0<τ<1$. We show how this problem can be reduced to the problem of transmitting messages over the substitution channel. Thereby, the maximal asymptotic rate of feedback insertion-deletion codes is completely established. The maximal asymptotic rate for the adversarial substitution channel has been partially determined by Berlekamp and later finished by Zigangirov. However, the analysis of the lower bound by Zigangirov is quite complicated. We revisit Zigangirov's result and present a more elaborate version of his proof.