一种基于训练的带反馈的未知信道通信方案

Aditya Mahajan, S. Tatikonda
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引用次数: 3

摘要

我们考虑一个具有无噪声反馈的通信系统,其中信道对编码器或解码器都是未知的。该通道属于已知的通道家族,并且随着时间的推移保持不变。利用无噪声反馈,编码器可以随时间学习信道并以等于信道实际实现容量的速率进行通信。因此,不知道信道并不影响容量。然而,分析错误指数(对于可变长度编码)更具挑战性。Tchamkerten和Telatar(2006)表明,对于某些频道族,不知道频道不会改变误差指数;对于其他家庭,不知道信道会导致误差指数的严格降低。通常,误差指数是未知的。我们还知道,简单的基于训练的方案具有较差的误差指数行为。在本文中,我们证明了一种基于智能训练的方案可以实现误差指数小于已知信道误差指数的乘因子。这表明,与普遍的看法相反,基于智能训练的方案保留了反馈的主要优势——在接近容量的速率下具有非零斜率的误差指数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A training based scheme for communicating over unknown channels with feedback
We consider a communication system with noiseless feedback where the channel is not known to the encoder or the decoder. The channel belongs to a known family of channels and remains constant over time. Using the noiseless feedback, the encoder can learn the channel over time and communicate at a rate equal to the capacity of the actual realization of the channel. Thus, not knowing the channel does not affect capacity. However, analyzing the error exponent (for variable length coding) is more challenging. Tchamkerten and Telatar (2006) showed that for certain families of channels, not knowing the channel does not change the error exponent; for other families, not knowing the channel results in a strict decrease in the error exponent. In general, the error exponent is not known. It is also known that simple training based schemes have poor error exponent behavior. In this paper, we show that a smart training based scheme can achieve an error exponent which is a multiplicative factor less than the error exponent for known channel. This shows that contrary to popular belief, smart training based schemes preserve the main advantage of feedback — an error exponent with non-zero slope at rates close to capacity.
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