We explore a scheme that enables the training of a deep neural network in a Federated Learning configuration over an additive white Gaussian noise channel. The goal is to create a low complexity, linear compression strategy, called PolarAir, that reduces the size of the gradient at the user side to lower the number of channel uses needed to transmit it. The suggested approach belongs to the family of compressed sensing techniques, yet it constructs the sensing matrix and the recovery procedure using multiple access techniques. Simulations show that it can reduce the number of channel uses by ∼30% when compared to conveying the gradient without compression. The main advantage of the proposed scheme over other schemes in the literature is its low time complexity. We also investigate the behavior of gradient updates and the performance of PolarAir throughout the training process to obtain insight on how best to construct this compression scheme based on compressed sensing.

Unsourced random access emerged as a novel wireless paradigm enabling massive device connectivity on the uplink. We consider quasi-static Rayleigh fading wherein the access point has multiple receive antennas and every mobile device a single transmit antenna. The objective is to construct a coding scheme that minimizes the energy-per-bit subject to a maximum probability of error given a fixed message length and a prescribed number of channel uses. Every message is partitioned into two parts: the first determines pilot values and spreading sequences; the remaining bits are encoded using a polar code. The transmitted signal contains two distinct sections. The first features pilots and the second is composed of spread modulated symbols. The receiver has three modules: an energy detector, tasked with recovering the set of active pilot sequences; a bank of Minimum Mean Square Error (MMSE) estimators acting on measurements at the receiver; and a polar list-decoder, which seeks to retrieve the coded information bits. A successive cancellation step is applied to subtract recovered codewords, before the residual signal is fed back to the decoder. Empirical evidence suggests that an appropriate combination of these ideas can outperform state-of-the-art coding techniques when the number of active users exceeds one hundred.

In this paper, we consider Wyner's [1] lossy distributed source coding problem of Fig. 1, for multivariate Gaussian distributed sources with square-error fidelity, when i) the side information, random variable (RV)$Y$, is available at the decoder only, and ii)$Y$is available at both the encoder and the decoder. We derive structural properties of optimal test channels that achieve the operational information rate distortion functions (RDFs) for i) and ii), i.e.,$\overline{R}(d)$and$R_{X\vert Y}(d)$, respectively. We also show there is no loss of compression if the side information$Y$is only available at the decoder, i.e.,$\overline{R}(d)=R_{X\vert Y}(d)$. This paper also points out that the two test channels of the RDF of the distributed remote source coding problem given in [2] and [3], do not generate Wyner's value of the RDF of scalar RVs, as one would expect; this observation implies that the results in [2, Theorem 4] and [3, Theorem 3A] should be read with caution.

We consider the approximate support recovery (ASR) task of inferring the support of a$K$-sparse vector$\mathrm{x}\in \mathbb{R}^{n}$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, which requires$\mathcal{O}(mn)$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.