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Achievable Error Exponents of One-Way and Two-Way AWGN Channels
IEEE Transactions on Information Theory ( IF 2.5 ) Pub Date : 2021-03-17 , DOI: 10.1109/tit.2021.3066855
Kenneth S. Palacio-Baus 1 , Natasha Devroye 1
Affiliation  

Achievable error exponents for the one-way with noisy feedback and two-way AWGN channels are derived for the transmission of a finite number of messages $M$ under almost sure (AS) and expected block (EXP) transmit power constraints. In the one-way setting under noisy AWGN feedback, under an AS power constraint, known linear and non-linear passive schemes are modified to incorporate AS constraints in the feedback link as well. In addition, a new active feedback scheme is presented in which the receiver feeds back the most likely pair of codewords, and the transmitter re-transmits which of these two was originally sent. This active feedback scheme outperforms one of the passive feedback schemes for all channel parameters; the linear scheme outperforms the others for low feedback noise variance. Under the EXP constraint, a known achievable error exponent for the transmission of two messages is generalized to any arbitrary but finite number of messages $M$ through the use of simplex codes and erasure decoding. In the two-way AWGN setting, each user has its own message to send in addition to (possibly) aiding in the transmission of feedback for the opposite direction. Two-way error exponent regions are defined and achievable error exponent regions are derived for the first time under both AS and EXP power constraints. For the presented achievability schemes, feedback or interaction leads to error exponent gains in one direction, possibly at the expense of a decrease in the error exponents attained in the other direction. The relationship between $M$ and $n$ supported by our achievable strategies is explored.

中文翻译:

单向和双向AWGN通道可实现的误差指数

导出具有噪声反馈的单向和双向AWGN信道可实现的误差指数,以传输有限数量的消息 $ M $ 在几乎确定(AS)和预期块(EXP)下的发射功率约束。在嘈杂的AWGN反馈下的单向设置中,在AS功率约束下,对已知的线性和非线性无源方案进行了修改,以在反馈链路中也包含AS约束。另外,提出了一种新的主​​动反馈方案,其中接收机反馈最可能的一对码字,而发射机重新发送这两个码字中的哪一个是最初发送的。对于所有通道参数而言,这种主动反馈方案都优于被动反馈方案之一。对于低反馈噪声方差,线性方案优于其他方案。在EXP约束下,用于传输两个消息的已知可实现错误指数被概括为任意数量但数量有限的消息 $ M $ 通过使用单纯形码和擦除解码。在双向AWGN设置中,每个用户都有自己的消息要发送(除了(可能)帮助发送反方向的反馈)。定义了双向误差指数区域,并且在AS和EXP功率约束下首次得出了可达到的误差指数区域。对于所提出的可实现性方案,反馈或交互作用会导致一个方向上的误差指数增益,可能以降低另一方向上获得的误差指数为代价。之间的关系 $ M $ $ n $ 探索了我们可行策略的支持。
更新日期:2021-04-23
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