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Limits on Support Recovery of Sparse Signals via Multiple-Access Communication Techniques

机译：通过多址通信技术支持恢复稀疏信号的限制

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摘要

In this paper, we consider the problem of exact support recovery of sparse signals via noisy linear measurements. The main focus is finding the sufficient and necessary condition on the number of measurements for support recovery to be reliable. By drawing an analogy between the problem of support recovery and the problem of channel coding over the Gaussian multiple-access channel (MAC), and exploiting mathematical tools developed for the latter problem, we obtain an information-theoretic framework for analyzing the performance limits of support recovery. Specifically, when the number of nonzero entries of the sparse signal is held fixed, the exact asymptotics on the number of measurements sufficient and necessary for support recovery is characterized. In addition, we show that the proposed methodology can deal with a variety of models of sparse signal recovery, hence demonstrating its potential as an effective analytical tool.
机译：在本文中，我们考虑了通过噪声线性测量来精确恢复稀疏信号的问题。主要重点是在测量数量上找到足够的必要条件以使支撑物恢复可靠。通过在支持恢复问题和高斯多址信道（MAC）上的信道编码问题之间进行类比，并利用针对后一个问题开发的数学工具，我们获得了一个信息理论框架，用于分析网络性能限制。支持恢复。具体地，当稀疏信号的非零项的数量保持固定时，表征了足以恢复支持所需的测量次数的精确渐近性。此外，我们证明了所提出的方法可以处理稀疏信号恢复的各种模型，从而证明了其作为有效分析工具的潜力。

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