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arXiv 2103.09373cs.ITmath.IT
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面向点对点、多址和随机接入信道的变长稀疏反馈码

Variable-Length Sparse Feedback Codes for Point-to-Point, Multiple Access, and Random Access Channels

Recep Can Yavas, Victoria Kostina, Michelle Effros

AI总结:

本文针对点对点、多址与随机接入无记忆信道设计仅需稀疏单比特反馈的变长停止反馈码,给出可达速率渐近近似及点对点情形逆定理。

摘要:

本文研究了点对点、多址和随机接入通信场景下无记忆信道的变长停止反馈码。所提出的码在点对点和多址信道中采用 $L$ 个解码时刻 $n_1, n_2, \dots, n_L$,而在最多有 $K$ 个活跃发射机的随机接入信道中采用 $KL + 1$ 个解码时刻。在点对点和多址信道中,解码器利用观测到的信道输出,在每个允许的解码时刻 $n_1, \dots, n_L$ 决定是否进行解码,并在每个时刻通过单比特反馈告知编码器是否停止发送。在随机接入场景中,解码器在时刻 $n_0$ 估计活跃发射机数量,如果认为存在 $k$ 个活跃发射机,则在解码时刻 $n_{k, 1}, \dots, n_{k, L}$ 之间进行选择。在所有情况下,允许解码时刻的选择都是码设计的一部分;在给定固定值 $L$ 时,对于给定码本大小和目标平均错误概率,选择允许的解码时刻以使期望解码时间最小。即使允许块长增长,每个场景中的数量 $L$ 也被假定为常数;因此所得码只需要稀疏反馈。核心结果是将可达速率作为错误概率、期望解码时间和解码时刻数量的函数给出渐近近似。对于点对点信道,本文还给出了具有均匀间隔解码时刻的变长停止反馈码的逆定理。

英文摘要:

This paper investigates variable-length stop-feedback codes for memoryless channels in point-to-point, multiple access, and random access communication scenarios. The proposed codes employ $L$ decoding times $n_1, n_2, \dots, n_L$ for the point-to-point and multiple access channels and $KL + 1$ decoding times for the random access channel with at most $K$ active transmitters. In the point-to-point and multiple access channels, the decoder uses the observed channel outputs to decide whether to decode at each of the allowed decoding times $n_1, \dots, n_L$, at each time telling the encoder whether or not to stop transmitting using a single bit of feedback. In the random access scenario, the decoder estimates the number of active transmitters at time $n_0$ and then chooses among decoding times $n_{k, 1}, \dots, n_{k, L}$ if it believes that there are $k$ active transmitters. In all cases, the choice of allowed decoding times is part of the code design; given fixed value $L$, allowed decoding times are chosen to minimize the expected decoding time for a given codebook size and target average error probability. The number $L$ in each scenario is assumed to be constant even when the blocklength is allowed to grow; the resulting code therefore requires only sparse feedback. The central results are asymptotic approximations of achievable rates as a function of the error probability, the expected decoding time, and the number of decoding times. A converse for variable-length stop-feedback codes with uniformly-spaced decoding times is included for the point-to-point channel.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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