This paper proposes a coding framework for capacity-region-achieving sparse regression (SR) codes over MIMO multiple-access channels (MIMO-MAC), where a single SR code is used for each user at the transmitter. With random semi-unitary dictionary matrices applied for encoding, multiple-access OAMP (MA-OAMP) enables reliable parallel interference cancellation (PIC) at the receiver. Theoretically, an optimal coding principle with the MA-OAMP receiver, which achieves the sum capacity and, in combination with time sharing, achieves the entire capacity region, is established as the guiding principle for designing capacity-region-achieving codes. Accordingly, a coding scheme for capacity-region-achieving SR codes is proposed via proper power allocation over the position-modulated signals.

Motivated by the recent interest in approximate message passing (AMP) for matrix-valued linear observations with superposition of multiple statistically asymmetric signal sources, we introduce a multi-source AMP framework in which the dictionary matrices associated with each signal source are drawn from a random semi-unitary ensemble (rather than the standard Gaussian matrix ensemble.) While a similar model has been explored by Vehkaperä, Kabashima, and Chatterjee (2016) using the replica method, here we present an AMP algorithm and provide a high-dimensional yet finite-sample analysis of its dynamics. As a proof of concept, we show the effectiveness of the proposed approach on the problem of message detection in an unsourced random access scenario in wireless communication.

We consider unsourced random access (uRA) in a cell-free (CF) user-centric wireless network, where a large number of potential users compete for a random access slot, while only a finite subset is active. The random access users transmit codewords of lengthLsymbols from a shared codebook, which are received byBgeographically distributed radio units (RUs), each equipped withMantennas. Our goal is to devise and analyze acentralizeddecoder to detect the transmitted messages (without prior knowledge of the active users) and estimate the corresponding channel state information. A specific challenge lies in the fact that, due to the geographically distributed nature of the CF network, there is no fixed correspondence between codewords and large-scale fading coefficients (LSFCs). This makes current activity detection approaches which make use of this fixed LSFC-codeword association not directly applicable. To overcome this problem, we propose a scheme where the access codebook is partitioned in location-based subcodes, such that users in a particular location make use of the corresponding subcode. The joint message detection and channel estimation is obtained via a novelApproximated Message Passing(AMP) algorithm for a linear superposition of matrix-valued sources corrupted by noise. The statistical asymmetry in the fading profile and message activity leads todifferent statisticsfor the matrix sources, which distinguishes the AMP formulation from previous cases. In the regime where the codebook size scales linearly withL, whileBandMare fixed, we present a rigorous high-dimensional (but finite-sample) analysis of the proposed AMP algorithm. Exploiting this, we then present a precise (and rigorous) large-system analysis of the message missed-detection and false-alarm rates, as well as the channel estimation mean-square error. The resulting system allows the seamless formation of user-centric clusters and very low latency beamformed uplink-downlink communication without explicit user-RU association, pilot allocation, and power control. This makes the proposed scheme highly appealing for low-latency random access communications in CF networks.

Motivated by the recent application of approximate message passing (AMP) to the analysis of convex optimizations in multi-class classifications [Loureiro, et. al., 2021], we present a convergence analysis of AMP dynamics with non-separable multivariate nonlinearities. As an application, we present a complete (and independent) analysis of the motivated convex optimization problem.

We propose an iterative algorithm for solving the Thouless-Anderson-Palmer (TAP) equations of Ising models with arbitrary rotation invariant (random) coupling matrices. In the (thermodynamic) limit of large-systems, we prove by means of the dynamical functional method that the proposed algorithm converges when the so-called de Almeida Thouless (AT) criterion is fulfilled. Moreover, we obtain an exact analytical expression for the rate of the convergence.

We study asymptotic properties of expectation propagation (EP) - a method for approximate inference originally developed in the field of machine learning. Applied to generalized linear models, EP iteratively computes a multivariate Gaussian approximation to the exact posterior distribution. The computational complexity of the repeated update of covariance matrices severely limits the application of EP to large problem sizes. In this study, we present a rigorous analysis by means of free probability theory that allows us to overcome this computational bottleneck if specific data matrices in the problem fulfill certain properties of asymptotic freeness. We demonstrate the relevance of our approach on the gene selection problem of a microarray dataset.

We investigate the capacity scaling of multiple-input-multiple-output systems with the system dimensions. To that end, we quantify how the mutual information varies when the number of antennas (at either the receiver or transmitter side) is altered. For a system comprising R receive and T transmit antennas with R > T, we find the following: by removing as many receive antennas as needed to obtain a square system (provided the channel matrices before and after the removal have full rank) the maximum resulting loss of mutual information over all signal-to-noise ratios (SNRs) depends only on R, T, and the matrix of left-singular vectors of the initial channel matrix, but not on its singular values. In particular, if the latter matrix is Haar distributed the ergodic rate loss is given by Σt=1TΣr=T+1R1/r-t nats. Under the same assumption, if T, R → ∞ with the ratio φ=ΔT/R fixed, the rate loss normalized by R converges almost surely to H(φ) bits with H(·) denoting the binary entropy function. We also quantify and study how the mutual information as a function of the system dimensions deviates from the traditionally assumed linear growth in the minimum of the system dimensions at high SNR.

We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix ensemble. By design, the fixed points of the algorithm obey the Thouless-Anderson-Palmer (TAP) equations corresponding to the ensemble. Using a dynamical functional approach we are able to derive an effective stochastic process for the marginal statistics of a single component of the dynamics. This allows us to design memory terms in the algorithm in such a way that the resulting fields become Gaussian random variables allowing for an explicit analysis. The asymptotic statistics of these fields are consistent with the replica ansatz of the compressed sensing problem.

We propose a hybrid message passing method for distributed cooperative localization and tracking of mobile agents. Belief propagation and mean field message passing are employed for, respectively, the motion-related and measurement-related parts of the factor graph. Using a Gaussian belief approximation, only three real values per message passing iteration have to be broadcast to neighboring agents. Despite these very low communication requirements, the estimation accuracy can be comparable to that of particle-based belief propagation.

Recently we presented the S-AMP approach, an extension of approximate message passing (AMP), to be able to handle general invariant matrix ensembles. In this contribution we extend S-AMP to non-linear observation models. We obtain generalized AMP (GAMP) as the special case when the measurement matrix has zero-mean iid Gaussian entries. Our derivation is based upon 1) deriving expectation-propagation-(EP)-like equations from the stationary-points equations of the Gibbs free energy under first- and second-moment constraints and 2) applying additive free convolution in free probability theory to get low-complexity updates for the second moment quantities.

We propose a novel iterative estimation algorithm for linear observation models called S-AMP. The fixed points of S-AMP are the stationary points of the exact Gibbs free energy under a set of (first- and second-) moment consistency constraints in the large system limit. S-AMP extends the approximate message-passing (AMP) algorithm to general matrix ensembles with a well-defined large system size limit. The generalization is based on the S-transform (in free probability) of the spectrum of the measurement matrix. Furthermore, we show that the optimality of S-AMP follows directly from its design rather than from solving a separate optimization problem as done for AMP.

This paper studies the asymptotic eigenvalue distribution (AED) and the mutual information of a multiuser (MU) multiple-input multiple output (MIMO) channel with a certain fraction of users experiencing line-of-sight. It shows that the AED of the channel matrix decomposes into two separate bulks for practically relevant parameter choices and differs very much from the common assumption of independent identically distributed (iid) entries which induces the quarter circle law. This happens even without antenna correlation at either side of the channel. In order to tackle this problem the paper makes use of recent developments in free probability theory which allow to deal with complex-valued eigenvalue distributions of non-Hermitian matrices by means of quaternions.