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arXiv 2105.12840cs.ITmath.IT
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基于编码的无源多址近似支持度恢复

Approximate Support Recovery using Codes for Unsourced Multiple Access

Michail Gkagkos, Asit Kumar Pradhan, Vamsi Amalladinne, Krishna Narayanan, Jean-Francois Chamberland, Costas N. Georghiades

摘要:

我们考虑近似支持恢复(ASR)的任务,从$m$噪声测量推断$K$ -稀疏向量${\bf x} \in \mathbb{R}^n$的支持。我们研究的情况下,$n$是大的,这排除了标准的压缩感知求解器的应用程序,从而需要具有较低的复杂性的解决方案。我们设计了一个方案,利用技术开发的无源多路访问的ASR。我们提出了两个解码算法的计算复杂性$\mathcal{O}(K^2 \log n+K \log n \log \log n)$和$\mathcal{O}(K^3 +K^2 \log n+ K \log n \log \log n)$每次迭代,分别。当使用$K \ll n$时,这比使用最小均方误差去噪器%(AMP-MMSE)的近似消息传递的复杂度低得多,AMP-MMSE需要每次迭代的$\mathcal{O}(mn)$操作。这种增益是以轻微的性能代价实现的。我们的研究结果表明,从多址%,如扩频,匹配滤波器接收机和代码的概念可以发挥重要作用,在测量方案的设计ASR。

英文摘要:

We consider the approximate support recovery (ASR) task of inferring the support of a $K$-sparse vector ${\bf x} \in \mathbb{R}^n$ from $m$ noisy measurements. We examine the case where $n$ is large, which precludes the application of standard compressed sensing solvers, thereby necessitating solutions with lower complexity. We design a scheme for ASR by leveraging techniques developed for unsourced multiple access. We present two decoding algorithms with computational complexities $\mathcal{O}(K^2 \log n+K \log n \log \log n)$ and $\mathcal{O}(K^3 +K^2 \log n+ K \log n \log \log n)$ per iteration, respectively. When $K \ll n$, this is much lower than the complexity of approximate message passing with a minimum mean squared error denoiser% (AMP-MMSE) ,which requires $\mathcal{O}(mn)$ operations per iteration. This gain comes at a slight performance cost. Our findings suggest that notions from multiple access %such as spreading, matched filter receivers and codes can play an important role in the design of measurement schemes for ASR.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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