Approximate Support Recovery Using Codes For Unsourced Multiple Access

We consider the approximate support recovery (ASR) task of inferring the support of a K-sparse vector x is an element of 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 O(K-2 log n + K log n log log n) and O(K-3 + K-2 log n + K log n log log n) per iteration, respectively. When K << n, this is much lower than the complexity of approximate message passing with a minimum mean squared error denoiser, which requires O(mn) operations per iteration. This gain comes at a slight performance cost. Our findings suggest that notions from multiple access can play an important role in the design of measurement schemes for ASR.