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Feedback in the Non-Asymptotic Regime

机译：非渐进体制下的反馈

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摘要

Without feedback, the backoff from capacity due to non-asymptotic blocklength can be quite substantial for blocklengths and error probabilities of interest in many practical applications. In this paper, novel achievability bounds are used to demonstrate that in the non-asymptotic regime, the maximal achievable rate improves dramatically thanks to variable-length coding and feedback. For example, for the binary symmetric channel with capacity $1/2$ the blocklength required to achieve 90% of the capacity is smaller than 200, compared to at least 3100 for the best fixed-blocklength code (even with noiseless feedback). Virtually all the advantages of noiseless feedback are shown to be achievable, even if the feedback link is used only to send a single signal informing the encoder to terminate the transmission (stop-feedback). It is demonstrated that the non-asymptotic behavior of the fundamental limit depends crucially on the particular model chosen for the “end-of-packet” control signal. Fixed-blocklength codes and related questions concerning communicating with a guaranteed delay are discussed, in which situation feedback is demonstrated to be almost useless even non-asymptotically.
机译：如果没有反馈，则对于许多实际应用中感兴趣的块长度和错误概率，由于非渐近块长度而导致的容量退缩可能会非常可观。在本文中，新颖的可实现性边界用于证明在非渐近状态下，由于可变长度编码和反馈，最大可实现率显着提高。例如，对于容量为$ 1/2 $的二进制对称信道，达到90％的容量所需的块长小于200，而对于最佳固定块长码，至少为3100（即使具有无噪声反馈）。即使反馈链接仅用于发送单个信号通知编码器终止传输（停止反馈），实际上也可以实现无噪声反馈的所有优势。已经证明，基本极限的非渐近行为主要取决于为“分组结束”控制信号选择的特定模型。讨论了固定块长码和与保证延迟通信有关的相关问题，在这种情况下，情况反馈被证明几乎是无用的，甚至是非渐近的。

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