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On Gaussian Channels With Feedback Under Expected Power Constraints and With Non-Vanishing Error Probabilities

机译：高斯信道上具有预期功率约束下的反馈并且具有零误差概率

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摘要

In this paper, we consider single- and multi-user Gaussian channels with feedback under expected power constraints and with non-vanishing error probabilities. In the first of two contributions, we study asymptotic expansions for the additive white Gaussian noise (AWGN) channel with feedback under the average error probability formalism. By drawing ideas from Gallager and Nakiboğlu’s work for the direct part and the meta-converse for the converse part, we establish the ε -capacity and show that it depends on ε in general and so the strong converse fails to hold. Furthermore, we provide bounds on the second-order term in the asymptotic expansion. We show that for any positive integer L , the second-order term is bounded between a term proportional to −ln(L)n (where ln(L)(⋅) is the L -fold nested logarithm function) and a term proportional to +(nlnn)1/2 , where n is the blocklength. The lower bound on the second-order term shows that feedback does provide an improvement in the maximal achievable rate over the case where no feedback is available. In our second contribution, we establish the ε -capacity region for the AWGN multiple access channel with feedback under the expected power constraint by combining ideas from hypothesis testing, information spectrum analysis, Ozarow’s coding scheme, and power control.
机译：在本文中，我们考虑具有预期功率约束下的反馈且误差概率不消失的单用户和多用户高斯信道。在两篇论文的第一篇中，我们研究了在平均误差概率形式主义下具有反馈的加性白高斯噪声（AWGN）通道的渐近展开。通过从Gallager和Nakiboğlu的工作中吸取直接部分的知识，并从逆向转换中获得元逆，我们建立了ε容量，并表明它通常取决于ε，因此强逆转换无法成立。此外，我们提供了渐近展开式中二阶项的界。我们表明，对于任何正整数L，二阶项都与-ln（L）n（其中ln（L）（⋅）是L倍嵌套对数函数）成比例的项和与+（nlnn）1/2，其中n是块长。二阶项的下限表明，与没有反馈可用的情况相比，反馈确实提供了最大可实现速率的改进。在我们的第二个贡献中，我们结合了假设测试，信息频谱分析，Ozarow编码方案和功率控制的思想，在预期功率约束下为AWGN多路访问信道建立了具有反馈能力的ε容量区域。

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