Memristor crossbars enable vector-matrix multiplication (VMM), and are promising for low-power applications. However, it can be difficult to write the memristor conductance values exactly. To improve the accuracy of VMM, we propose a scheme based on low-rank matrix approximation. Specifically, singular value decomposition (SVD) is first applied to obtain a low-rank approximation of the target matrix, which is then factored into a pair of smaller matrices. Subsequently, a two-step serial VMM is executed, where the stochastic write errors are mitigated through step-wise averaging. To evaluate the performance of the proposed scheme, we derive a general expression for the resulting computation error and provide an asymptotic analysis under a prescribed singular-value profile, which reveals how the error scales with matrix size and rank. Both analytical and numerical results confirm the superiority of the proposed scheme compared with the benchmark scheme.

Consider a point-to-point communication system in which the transmitter holds a binary message of length $m$ and transmits a corresponding codeword of length $n$. The receiver's goal is to recover a Boolean function of that message, where the function is unknown to the transmitter, but chosen from a known class $F$. We are interested in the asymptotic relationship of $m$ and $n$: given $n$, how large can $m$ be (asymptotically), such that the value of the Boolean function can be recovered reliably? This problem generalizes the identification-via-channels framework introduced by Ahlswede and Dueck. We formulate the notion of computation capacity, and derive achievability and converse results for selected classes of functions $F$, characterized by the Hamming weight of functions. Our obtained results are tight in the sense of the scaling behavior for all cases of $F$ considered in the paper.

We study communication over a Gaussian multiple-access channel (MAC) with two types of transmitters: Digital transmitters hold a message from a discrete set that needs to be communicated to the receiver with vanishing error probability. Analog transmitters hold sequences of analog values. Some functions of these distributed values (but not the values themselves) need to be conveyed to the receiver, subject to a fidelity criterion such as mean squared error (MSE) or a certain maximum error with given confidence. For the case in which the computed function for the analog transmitters is a sum of values in$[-1,1]$, we derive inner and outer bounds for the tradeoff of digital and analog rates of communication under peak and average power constraints for digital transmitters and a peak power constraint for analog transmitters. We then extend the achievability result to a class of functions that includes all linear and some non-linear functions. This extended scheme works over fading channels as long as full channel state information is available at the transmitter. The practicality of our proposed communication scheme is shown in channel simulations that use a version of the scheme based on low density parity check (LDPC) coding. We evaluate the system performance for different block lengths and Gaussian as well as non-Gaussian noise distributions.

We propose a new proof method for direct coding theorems for wiretap channels where the eavesdropper has access to a quantum version of the transmitted signal on an infinite-dimensional Hilbert space and the legitimate parties communicate through a classical channel or a classical input, quantum output (cq) channel. The transmitter input can be subject to an additive cost constraint, which specializes to the case of an average energy constraint. This method yields errors that decay exponentially with increasing block lengths. Moreover, it provides a guarantee of a quantum version of semantic security, which is an established concept in classical cryptography and physical layer security. Therefore, it complements existing works which either do not prove the exponential error decay or use weaker notions of security. The main part of this proof method is a direct coding result on channel resolvability which states that there is only a doubly exponentially small probability that a standard random codebook does not solve the channel resolvability problem for the cq channel. Semantic security has strong operational implications meaning essentially that the eavesdropper cannot use its quantum observation to gather any meaningful information about the transmitted signal. We also discuss the connections between semantic security and various other established notions of secrecy.

Vico et al. suggest a fast algorithm for computing volume potentials, beneficial to fields with problems requiring the solution of the free-space Poisson’s equation, such as beam and plasma physics. Currently, the standard is the algorithm of Hockney and Eastwood, with second order in convergence at best. The algorithm proposed by Vico et al. converges spectrally for sufficiently smooth functions, i.e., faster than any fixed order in the number of grid points. We implement a performance portable version of the traditional Hockney-Eastwood and the novel Vico-Greengard Poisson solver as part of the Independent Parallel Particle Layer (IPPL) library. For sufficiently smooth source functions, the Vico-Greengard algorithm achieves higher accuracy than the Hockney-Eastwood method with the same grid size, reducing the computational demands of high-resolution simulations since one could use coarser grids to achieve them. Additionally, we propose an improvement to the Vico-Greengard method which further reduces its memory footprint. This is important for GPUs, which have limited memory, and should be taken into account when selecting numerical algorithms for performance portable codes. Finally, we showcase performance through GPU and CPU scaling studies on the Perlmutter (NERSC) supercomputer, with efficiencies staying above 50% in the strong scaling case. To showcase portability, we also run the scaling studies on the Alps supercomputer at CSCS, Switzerland and the GPU partition of the Lumi supercomputer at CSC, Finland.

We study communication over a Gaussian multiple-access channel (MAC) with two types of transmitters: Digital transmitters hold a message from a discrete set that needs to be communicated to the receiver. Analog transmitters hold sequences of analog values, and some function of these distributed values (but not the values themselves) need to be conveyed to the receiver. For the digital messages, it is required that they can be decoded error free at the receiver with high probability while the recovered analog function values have to satisfy a fidelity criterion such as an upper bound on mean squared error (MSE) or a certain maximum error with a given confidence. For the case in which the computed function for the analog transmitters is a sum of values in [-1, 1], we derive inner and outer bounds for the tradeoff of digital and analog rates of communication under peak and average power constraints for digital transmitters and a peak power constraint for analog transmitters. We then extend the achievability part of our result to a larger class of functions that includes all linear, but also some non-linear functions.

We introduce the concept of inverse feasibility for linear forward models as a tool to enhance Over-the-Air (OTA) federated learning (FL) algorithms. Inverse feasibility is defined as an upper bound on the condition number of the forward operator as a function of its parameters. We analyze an existing OTA FL model using this definition, identify areas for improvement, and propose a new OTA FL model. Numerical experiments illustrate the main implications of the theoretical results. The proposed framework, which is based on inverse problem theory, can potentially complement existing notions of security and privacy by providing additional desirable characteristics to networks.

Lagrange coded computation (LCC) is essential to solving problems about matrix polynomials in a coded distributed fashion; nevertheless, it can only solve the problems that are representable as matrix polynomials. In this paper, we propose AICC, an AI-aided learning approach that is inspired by LCC but also uses deep neural networks (DNNs). It is appropriate for coded computation of more general functions. Numerical simulations demonstrate the suitability of the proposed approach for the coded computation of different matrix functions that are often utilized in digital signal processing.

We propose a new proof method for direct coding theorems for wiretap channels where the eavesdropper has access to a quantum version of the transmitted signal on an infinite dimensional Hilbert space. This method yields errors that decay exponentially with increasing block lengths. Moreover, it provides a guarantee of a quantum version of semantic security, which is an established concept in classical cryptography and physical layer security. Semantic security has strong operational implications meaning essentially that the eavesdropper cannot use its quantum observation to gather any meaningful information about the transmitted signal. Therefore, it complements existing works which either do not prove the exponential error decay or use weaker notions of security. The main part of this proof method is a direct coding result on channel resolvability which states that there is only a doubly exponentially small probability that a standard random codebook does not solve the channel resolvability problem for the classical-quantum channel.

We propose a new method to protect Over-The-Air (OTA) computation schemes against passive eavesdropping. Our method uses a friendly jammer whose signal is – contrary to common intuition – stronger at the legitimate receiver than it is at the eavesdropper. It works for a large class of analog OTA computation schemes and we give two examples for such schemes that are contained in this class. The key ingredients in proving the security guarantees are a known result on channel resolvability and a generalization of existing results on coding for compound channels.

This paper addresses the problem of Over-The-Air (OTA) computation in wireless networks which has the potential to realize huge efficiency gains for instance in training of distributed ML models. We provide non-asymptotic, theoretical guarantees for OTA computation in fast-fading wireless channels where the fading and noise may be correlated. The distributions of fading and noise are not restricted to Gaussian distributions, but instead are assumed to follow a distribution in the more general sub-gaussian class. Furthermore, our result does not make any assumptions on the distribution of the sources and therefore, it can, e.g., be applied to arbitrarily correlated sources. We illustrate our analysis with numerical evaluations for OTA computation of two example functions in large wireless networks: the arithmetic mean and the Euclidean norm.

We characterize the resolvability region for a large class of point-to-point channels with continuous alphabets. In our direct result, we prove not only the existence of good resolvability codebooks, but adapt an approach based on the Chernoff-Hoeffding bound to the continuous case showing that the probability of drawing an unsuitable codebook is doubly exponentially small. For the converse part, we show that our previous elementary result carries over to the continuous case easily under some mild continuity assumption.

Flash analog-to-digital converters can be built using small (and fast) low-precision comparators with unpredictable thresholds followed by a digital look-up table to correct the output. The look-up table should store digital codes with higher precision than the nominal resolution of the converter. The effective resolution of such a scheme with N comparators is roughly log2(N) - 1 bits. The concept is demonstrated by a chip that achieves almost 7 bit resolution with 256 low-precision comparators

It has been observed that a linear-feedback shift-register (LFSR) sequence can be synchronized by feeding the modulated sequence into a "soft" (or "analog") version of the LFSR. In this correspondence, the "soft LFSR" is derived as forward-only message passing in the corresponding factor graph. A continous-time analog (suitable for realization as a clockless electronic circuit) is then given of both the LFSR and the soft LFSR. A connection is thus established between statistical state estimation and the phenomenon of entrainment of dynamical systems, which opens the prospect of deriving dynamical systems (such as electronic circuits) with strong entrainment capabilities from more powerful message passing algorithms