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A Proof of the Strong Converse Theorem for Gaussian Multiple Access Channels

机译：高斯多路访问信道的强逆定理的证明

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摘要

We prove the strong converse for the -source Gaussian multiple access channel. In particular, we show that any rate tuple that can be supported by a sequence of codes with asymptotic average error probability <1 must lie in the Cover–Wyner capacity region. Our proof consists of the following. First, we perform an expurgation step to convert any given sequence of codes with asymptotic average error probability <1 to codes with asymptotic maximal error probability <1. Second, we quantize the input alphabets with an appropriately chosen resolution. Upon quantization, we apply the wringing technique (by Ahlswede) on the quantized inputs to obtain further subcodes from the subcodes obtained in the expurgation step, so that the resultant correlations among the symbols transmitted by the different sources vanish as the blocklength grows. Finally, we derive upper bounds on achievable sum-rates of the subcodes in terms of the type-II error of a binary hypothesis test. These upper bounds are then simplified through judicious choices of auxiliary output distributions. Our strong converse result carries over to the Gaussian interference channel under strong interference as long as the sum of the two asymptotic average error probabilities <1.
机译：我们证明了-source高斯多路访问通道的强大优势。特别是，我们表明，渐近平均错误概率小于1的一系列代码所能支持的任何速率元组都必须位于Cover–Wyner容量区域。我们的证明包括以下内容。首先，我们执行清除步骤，将渐近平均错误概率<1的任何给定代码序列转换为渐近最大错误概率<1的代码。其次，我们使用适当选择的分辨率对输入字母进行量化。在量化时，我们在量化输入上应用了拧紧技术（由Ahlswede进行处理），以从在抽取步骤中获得的子代码中获取更多子代码，以使随着块长的增长，不同源传输的符号之间的相关性消失。最后，根据二元假设检验的II类错误，得出子码可达到的总和的上限。然后，通过明智地选择辅助输出分布来简化这些上限。只要两个渐近平均误差概率之和<1，我们的强逆结果就会在强干扰下延续到高斯干扰信道。

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