Information Theoretic Limits for Standard and One-Bit Compressed Sensing with Graph-Structured Sparsity

In this paper, we analyze the information theoretic lower bound on the necessary number of samples needed for recovering a sparse signal under different compressed sensing settings. We focus on the weighted graph model, a model-based framework proposed by Hegde et al. (2015), for standard compressed sensing as well as for one-bit compressed sensing. We study both the noisy and noiseless regimes. Our analysis is general in the sense that it applies to any algorithm used to recover the signal. We carefully construct restricted ensembles for different settings and then apply Fano's inequality to establish the lower bound on the necessary number of samples. Furthermore, we show that our bound is tight for one-bit compressed sensing, while for standard compressed sensing, our bound is tight up to a logarithmic factor of the number of non-zero entries in the signal

One-Bit ExpanderSketch for One-Bit Compressed Sensing

Is it possible to obliviously construct a set of hyperplanes H such that you can approximate a unit vector x when you are given the side on which the vector lies with respect to every h in H? In the sparse recovery literature, where x is approximately k-sparse, this problem is called one-bit compressed sensing and has received a fair amount of attention the last decade. In this paper we obtain the first scheme that achieves almost optimal measurements and sublinear decoding time for one-bit compressed sensing in the non-uniform case. For a large range of parameters, we improve the state of the art in both the number of measurements and the decoding time

User Activity Detection in Massive Random Access: Compressed Sensing vs. Coded Slotted ALOHA

Machine-type communication services in mobile cel- lular systems are currently evolving with an aim to efficiently address a massive-scale user access to the system. One of the key problems in this respect is to efficiently identify active users in order to allocate them resources for the subsequent transmissions. In this paper, we examine two recently suggested approaches for user activity detection: compressed-sensing (CS) and coded slotted ALOHA (CSA), and provide their comparison in terms of performance vs resource utilization. Our preliminary results show that CS-based approach is able to provide the target user activity detection performance with less overall system resource utilization. However, this comes at a price of lower energy- efficiency per user, as compared to CSA-based approach.Comment: Accepted for presentation at IEEE SPAWC 201