We consider a point-to-point communication system, where in addition to the encoder and the decoder, there is a helper that observes non-causally the realization of the noise vector and provides a (lossy) rate-$R_{\mbox{\tiny h}}$ description of it to the encoder ($R_{\mbox{\tiny h}} < \infty$). While Lapidoth and Marti (2020) derived coding theorems, associated with achievable channel-coding rates (of the main encoder) for this model, here our focus is on error exponents. We consider both continuous-alphabet, additive white Gaussian channels and finite-alphabet, modulo-additive channels, and for each one of them, we study the cases of both fixed-rate and variable-rate noise descriptions by the helper. Our main finding is that, as long as the channel-coding rate, $R$, is below the helper-rate, $R_{\mbox{\tiny h}}$, the achievable error exponent is unlimited (i.e., it can be made arbitrarily large), and in some of the cases, it is even strictly infinite (i.e., the error probability can be made strictly zero). However, in the range of coding rates $(R_{\mbox{\tiny h}},R_{\mbox{\tiny h}}+C_0)$, $C_0$ being the ordinary channel capacity (without help), the best achievable error exponent is finite and strictly positive, although there is a certain gap between our upper bound (converse bound) and lower bound (achievability) on the highest achievable error exponent. This means that the model of encoder-assisted communication is essentially equivalent to a model, where in addition to the noisy channel between the encoder and decoder, there is also a parallel noiseless bit-pipe of capacity $R_{\mbox{\tiny h}}$. We also extend the scope to the Gaussian multiple access channel (MAC) and characterize the rate sub-region, where the achievable error exponent is unlimited or even infinite.

中文翻译：

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编码器辅助通信系统的误差指数

我们考虑一种点对点通信系统，其中除了编码器和解码器外，还有一个帮助程序，该帮助程序非因果地观察噪声矢量的实现，并提供（有损）速率-$ R _ {\ mbox { \ tiny h}} $对编码器的描述（$ R _ {\ mbox {\ tiny h}} <\ infty $）。尽管Lapidoth和Marti（2020）得出了与该模型可实现的（主编码器的）信道编码率相关的编码定理，但此处我们的重点是误差指数。我们同时考虑了连续字母，加性白高斯通道和有限字母，模加性通道，并针对其中每个通道，研究了辅助方法对固定速率和可变速率噪声的描述。我们的主要发现是，只要通道编码率$ R $低于帮助者率$ R _ {\ mbox {\ tiny h}} $，可实现的错误指数是无限的（即可以任意增大），在某些情况下甚至可以严格地无限（即可以将错误概率严格地设为零）。但是，在编码速率$（R _ {\ mbox {\ tiny h}}，R _ {\ mbox {\ tiny h}} + C_0）$的范围内，$ C_0 $是普通信道容量（无帮助），最佳可实现误差指数是有限的且严格为正，尽管在最高可实现误差指数的上限（逆界）与下限（可实现性）之间存在一定差距。这意味着编码器辅助通信的模型基本上等同于一个模型，在该模型中，除了编码器和解码器之间的噪声通道外，还存在容量为$ R _ {\ mbox {\ tiny h }} $。