基于非编码方案的匹配多用户高斯信源信道通信
Matched Multiuser Gaussian Source-Channel Communications via Uncoded Schemes
摘要：
我们调查未编码的计划是否是最佳的高斯源多用户高斯信道。特别地，我们考虑两个问题：第一个是在高斯广播信道上发送相关高斯源，其中每个接收机只对一个源分量感兴趣（或源的一个特定线性函数）在均方误差失真度量下的估计;第二种是在高斯多址信道上发送相关的高斯源，其中每个发射机观测到源的噪声组合，并且接收机希望在均方误差失真度量下重构各个源分量（或各个线性函数）。结果表明，当信道参数满足一定的一般条件时，诱导的失真元组在可达失真区域的边界上，因此是最优的。而不是按照传统的方法，试图表征可实现的失真区域，我们问的问题是否以及如何匹配可以有效地确定。这种决策问题的制定有助于规避困难的优化问题，往往嵌入在区域表征问题，它也使我们专注于临界条件的外边界，使不等式成为平等，有效地解耦成几个简单的子问题的整体问题。以前未知的文献中的最优性结果得到使用这种新的方法。作为副产品的调查，新的外边界推导出这两个问题。
英文摘要：
We investigate whether uncoded schemes are optimal for Gaussian sources on multiuser Gaussian channels. Particularly, we consider two problems: the first is to send correlated Gaussian sources on a Gaussian broadcast channel where each receiver is interested in reconstructing only one source component (or one specific linear function of the sources) under the mean squared error distortion measure; the second is to send correlated Gaussian sources on a Gaussian multiple-access channel, where each transmitter observes a noisy combination of the source, and the receiver wishes to reconstruct the individual source components (or individual linear functions) under the mean squared error distortion measure. It is shown that when the channel parameters match certain general conditions, the induced distortion tuples are on the boundary of the achievable distortion region, and thus optimal. Instead of following the conventional approach of attempting to characterize the achievable distortion region, we ask the question whether and how a match can be effectively determined. This decision problem formulation helps to circumvent the difficult optimization problem often embedded in region characterization problems, and it also leads us to focus on the critical conditions in the outer bounds that make the inequalities become equalities, which effectively decouple the overall problem into several simpler sub-problems. Optimality results previously unknown in the literature are obtained using this novel approach. As a byproduct of the investigation, novel outer bounds are derived for these two problems.
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