论文标题
关于编码辅助通信系统的错误指数
On Error Exponents of Encoder-Assisted Communication Systems
论文作者
论文摘要
我们考虑了一个点对点的通信系统，除编码器和解码器外，还有一个助手，从非涉及噪声向量的实现，并提供了（损失的）速率-R _ {\ mbox {\ mbox {\ tiny h}} $描述eNCODER（$ r _ fobbobs）<mbox <mbox <mbox <mbox <mbox <\ tiny <\ tiny \ tiny hyty hyty hyty hyty hyty hyty hyty h。尽管Lapidoth和Marti（2020）得出了与该模型的可实现的通道编码率（主要编码器）相关的编码定理，但这里我们的重点是错误指数。我们同时考虑连续的字母，添加剂白色高斯通道和有限词组，模量添加的通道，对于每个通道，我们都会研究辅助人员的固定利率和可变速率噪声描述的案例。我们的主要发现是，只要通道编码速率$ r $在辅助率下方，$ r _ {\ mbox {\ mbox {\ tiny h}} $，可实现的错误指数是无效的（即可以任意地使其变大），并且在某些情况下，它甚至可以严格地概括（即严格概括）（即错误）。但是，在编码范围内，$（r _ {\ mbox {\ tiny h}}，r _ {\ mbox {\ mbox {\ tiny H}}+C_0）$，$ c_0 $是普通通道容量（无用帮助），最佳范围是有限的，尽管有有限的范围，但我们的上点是一定的（CONVERIED）（我们的averve and converse and converse and converse and converse and converse（converse and converse and converse and converse and converse and）可实现的错误指数。这意味着编码器辅助通信的模型基本上等同于模型，除了编码器和解码器之间的嘈杂通道外，还有一个平行的无噪声容量$ r _ {\ mbox {\ mbox {\ tiny h}}} $。我们还将范围扩展到高斯多访问通道（MAC），并表征速率子区域，其中可实现的误差指数是无限甚至无限的。
We consider a point-to-point communication system, where in addition to the encoder and the decoder, there is a helper that observes non-causally the realization of the noise vector and provides a (lossy) rate-$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.
