反馈插入-删除代码

IF 0.5 4区 计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS
Maringer, G., Polyanskii, N. A., Vorobyev, I. V., Welter, L.
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引用次数: 0

摘要

提出了一种新的带有反馈的对抗性插入-删除信道信息传输问题。假设编码器通过可以删除一些符号并可以插入一些附加符号的信道逐个传输\(n\)二进制符号。在每次传输之后,编码器收到关于在前一次传输中发生的插入或删除的通知,并且可以相应地调整编码策略。目标是设计一个编码器,在假设删除和插入的总数受\(\tau n\), \(0<\tau<1\)限制的情况下,能够传输尽可能多的无错误信息。我们将展示如何将此问题简化为通过替代通道传输消息的问题。从而完全建立了反馈插入-删除码的最大渐近率。对抗性替代通道的最大渐近速率部分由Berlekamp确定,后来由zigangrov完成。然而,zigangrov对下界的分析是相当复杂的。我们重新审视zigangrov的结果,并提出一个更详尽的证明版本。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Feedback Insertion-Deletion Codes

A new problem of transmitting information over the adversarial insertion-deletion channel with feedback is introduced. Assume 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 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 \(\tau n\), \(0<\tau<1\). 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 completed 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.

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来源期刊
Problems of Information Transmission
Problems of Information Transmission 工程技术-计算机:理论方法
CiteScore
2.00
自引率
25.00%
发文量
10
审稿时长
>12 weeks
期刊介绍: Problems of Information Transmission is of interest to researcher in all fields concerned with the research and development of communication systems. This quarterly journal features coverage of statistical information theory; coding theory and techniques; noisy channels; error detection and correction; signal detection, extraction, and analysis; analysis of communication networks; optimal processing and routing; the theory of random processes; and bionics.
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