arXiv subjects

Ori Shental

Publications and source records attributed to Ori Shental.

At least 19 recordsLinked to original sources

arXiv2023

Transformer-Based Neural Surrogate for Link-Level Path Loss Prediction from Variable-Sized Maps

Estimating path loss for a transmitter-receiver location is key to many use-cases including network planning and handover. Machine learning has become a popular tool to predict wireless channel properties based on map data. In this work, we present a transformer-based neural network architecture that enables predicting link-level properties from maps of various dimensions and from sparse measurements. The map contains information about buildings and foliage. The transformer model attends to the regions that are relevant for path loss prediction and, therefore, scales efficiently to maps of different size. Further, our approach works with continuous transmitter and receiver coordinates without relying on discretization. In experiments, we show that the proposed model is able to efficiently learn dominant path losses from sparse training data and generalizes well when tested on novel maps.

cs.LG↗

arXiv2020

The Penalty in Scaling Exponent for Polar Codes is Analytically Approximated by the Golden Ratio

The polarization process of conventional polar codes in binary erasure channel (BEC) is recast to the Domany-Kinzel cellular automaton model of directed percolation in a tilted square lattice. Consequently, the former's scaling exponent, $μ$, can be analogously expressed as the inverse of the percolation critical exponent, $β$. Relying on the vast percolation theory literature and the best known numerical estimate for $β$, the scaling exponent can be easily estimated as $μ_{\text{num}}^{\text{perc}}\simeq1/0.276486(8)\simeq3.617$, which is only about $0.25\%$ away from the known exponent computation from coding theory literature based on numerical approximation, $μ_{\text{num}}\simeq3.627$. Remarkably, this numerical result for the critical exponent, $β$, can be analytically approximated (within only $0.028\%$) leading to the closed-form expression for the scaling exponent $μ\simeq2+φ=2+1.618\ldots\simeq3.618$, where $φ\triangleq(1+\sqrt{5})/2$ is the ubiquitous golden ratio. As the ultimate achievable scaling exponent is quadratic, this implies that the penalty for polar codes in BEC, in terms of the scaling exponent, can be very well estimated by the golden ratio, $φ$, itself.

cs.IT↗

arXiv2020

"Machine LLRning": Learning to Softly Demodulate

Soft demodulation, or demapping, of received symbols back into their conveyed soft bits, or bit log-likelihood ratios (LLRs), is at the very heart of any modern receiver. In this paper, a trainable universal neural network-based demodulator architecture, dubbed "LLRnet", is introduced. LLRnet facilitates an improved performance with significantly reduced overall computational complexity. For instance for the commonly used quadrature amplitude modulation (QAM), LLRnet demonstrates LLR estimates approaching the optimal log maximum a-posteriori inference with an order of magnitude less operations than that of the straightforward exact implementation. Link-level simulation examples for the application of LLRnet to 5G-NR and DVB-S.2 are provided. LLRnet is a (yet another) powerful example for the usefulness of applying machine learning to physical layer design.

cs.IT↗

arXiv2020

Prefix-Free Code Distribution Matching for 5G New Radio

We use prefix-free code distribution matching (PCDM) for rate matching (RM) in some 5G New Radio (NR) deployment scenarios, realizing a wide range of information rates from 1.4 to 6.0 bit/symbol in fine granularity of 0.2 bit/symbol. We study the performance and implementation of the PCDM-based RM, in comparison with the low-density parity-check (LDPC)-based RM, as defined in the 5G NR standard. Simulations in the additive white Gaussian noise channel show that up to 2.16 dB gain in the signal-to-noise ratio can be obtained with the PCDM-based RM at a block error rate of 10-2 when compared to LDPC-based RM in the tested scenarios, potentially at a smaller hardware cost.

eess.SP↗

arXiv2018

Sparse NOMA: A Closed-Form Characterization

Understanding fundamental limits of the various technologies suggested for future 5G and beyond cellular systems is crucial for developing efficient state-of-the-art designs. A leading technology of major interest is non-orthogonal multiple-access (NOMA). In this paper, we derive an explicit rigorous closed-form analytical expression for the optimum spectral efficiency in the large-system limit of regular sparse NOMA, where only a fixed and finite number of orthogonal resources are allocated to any designated user, and vice versa. The basic Verdú-Shamai formula for (dense) randomly-spread code-division multiple-access (RS-CDMA) turns out to coincide with the limit of the derived expression, when the number of orthogonal resources per user grows large. Furthermore, regular sparse NOMA is rigorously shown to be spectrally more efficient than RS-CDMA across the entire system load range. It may therefore serve as an efficient means for reducing the throughput gap to orthogonal transmission in the underloaded regime, and to the ultimate Cover-Wyner bound in overloaded systems. The results analytically reinforce preliminary conclusions in [1], which mostly relied on heuristics and numerical observations. The spectral efficiency is also derived in closed form for the suboptimal linear minimum-mean-square-error (LMMSE) receiver, which again extends the corresponding Verdú-Shamai LMMSE formula to regular sparse NOMA.

cs.IT↗

arXiv2017

Massive BLAST: An Architecture for Realizing Ultra-High Data Rates for Large-Scale MIMO

A detection scheme for uplink massive MIMO, dubbed massive-BLAST or M-BLAST, is proposed. The derived algorithm is an enhancement of the well-known soft parallel interference cancellation. Using computer simulations in massive MIMO application scenarios, M-BLAST is shown to yield a substantially better error performance with reduced complexity, compared to the benchmark alternative of a one-shot linear detector, as well as the original sequential V-BLAST. Hence, M-BLAST may serve as a computationally efficient means to exploit the large number of antennas in massive MIMO.

cs.IT↗

arXiv2017

Low-Density Code-Domain NOMA: Better Be Regular

A closed-form analytical expression is derived for the limiting empirical squared singular value density of a spreading (signature) matrix corresponding to sparse low-density code-domain (LDCD) non-orthogonal multiple-access (NOMA) with regular random user-resource allocation. The derivation relies on associating the spreading matrix with the adjacency matrix of a large semiregular bipartite graph. For a simple repetition-based sparse spreading scheme, the result directly follows from a rigorous analysis of spectral measures of infinite graphs. Turning to random (sparse) binary spreading, we harness the cavity method from statistical physics, and show that the limiting spectral density coincides in both cases. Next, we use this density to compute the normalized input-output mutual information of the underlying vector channel in the large-system limit. The latter may be interpreted as the achievable total throughput per dimension with optimum processing in a corresponding multiple-access channel setting or, alternatively, in a fully-symmetric broadcast channel setting with full decoding capabilities at each receiver. Surprisingly, the total throughput of regular LDCD-NOMA is found to be not only superior to that achieved with irregular user-resource allocation, but also to the total throughput of dense randomly-spread NOMA, for which optimum processing is computationally intractable. In contrast, the superior performance of regular LDCD-NOMA can be potentially achieved with a feasible message-passing algorithm. This observation may advocate employing regular, rather than irregular, LDCD-NOMA in 5G cellular physical layer design.

cs.IT↗

arXiv2017

Sparse Representation of White Gaussian Noise with Application to L0-Norm Decoding in Noisy Compressed Sensing

The achievable and converse regions for sparse representation of white Gaussian noise based on an overcomplete dictionary are derived in the limit of large systems. Furthermore, the marginal distribution of such sparse representations is also inferred. The results are obtained via the Replica method which stems from statistical mechanics. A direct outcome of these results is the introduction of sharp threshold for $\ell_{0}$-norm decoding in noisy compressed sensing, and its mean-square error for underdetermined Gaussian vector channels.

cs.IT↗

arXiv2010

An efficient CDMA decoder for correlated information sources

We consider the detection of correlated information sources in the ubiquitous Code-Division Multiple-Access (CDMA) scheme. We propose a message-passing based scheme for detecting correlated sources directly, with no need for source coding. The detection is done simultaneously over a block of transmitted binary symbols (word). Simulation results are provided demonstrating a substantial improvement in bit-error-rate in comparison with the unmodified detector and the alternative of source compression. The robustness of the error-performance improvement is shown under practical model settings, including wrong estimation of the generating Markov transition matrix and finite-length spreading codes.

cs.IT↗

arXiv2009

Mutual information via thermodynamics: Three different approaches

Three different approaches to derive mutual information via thermodynamics are presented where the temperature-dependent energy is given by: (a) $β\mathcal{E} = -\ln[P(X,Y)]$, (b) $β\mathcal{E} =-\ln[P(Y|X)]$ or (c) $β\mathcal{E} =-\ln[P(X|Y)]$. All approaches require the extension of the traditional physical framework and the modification of the 2nd law of thermodynamics. A realization of a physical system with an effective temperature-dependent Hamiltonian is discussed followed by a suggestion of a physical information-heat engine.

cond-mat.stat-mech↗

arXiv2009

Information and multiaccess interference in a complexity-constrained vector channel

Rodrigo de Miguel et al 2007 J. Phys. A: Math. Theor. 40 5241-5260: A noisy vector channel operating under a strict complexity constraint at the receiver is introduced. According to this constraint, detected bits, obtained by performing hard decisions directly on the channel's matched filter output, must be the same as the transmitted binary inputs. An asymptotic analysis is carried out using mathematical tools imported from the study of neural networks, and it is shown that, under a bounded noise assumption, such complexity-constrained channel exhibits a non-trivial Shannon-theoretic capacity. It is found that performance relies on rigorous interference-based multiuser cooperation at the transmitter and that this cooperation is best served when all transmitters use the same amplitude.

cs.IT↗

arXiv2008

Distributed Kalman Filter via Gaussian Belief Propagation

Recent result shows how to compute distributively and efficiently the linear MMSE for the multiuser detection problem, using the Gaussian BP algorithm. In the current work, we extend this construction, and show that operating this algorithm twice on the matching inputs, has several interesting interpretations. First, we show equivalence to computing one iteration of the Kalman filter. Second, we show that the Kalman filter is a special case of the Gaussian information bottleneck algorithm, when the weight parameter $β= 1$. Third, we discuss the relation to the Affine-scaling interior-point method and show it is a special case of Kalman filter. Besides of the theoretical interest of this linking estimation, compression/clustering and optimization, we allow a single distributed implementation of those algorithms, which is a highly practical and important task in sensor and mobile ad-hoc networks. Application to numerous problem domains includes collaborative signal processing and distributed allocation of resources in a communication network.

cs.IT↗

arXiv2008

Polynomial Linear Programming with Gaussian Belief Propagation

Interior-point methods are state-of-the-art algorithms for solving linear programming (LP) problems with polynomial complexity. Specifically, the Karmarkar algorithm typically solves LP problems in time O(n^{3.5}), where $n$ is the number of unknown variables. Karmarkar's celebrated algorithm is known to be an instance of the log-barrier method using the Newton iteration. The main computational overhead of this method is in inverting the Hessian matrix of the Newton iteration. In this contribution, we propose the application of the Gaussian belief propagation (GaBP) algorithm as part of an efficient and distributed LP solver that exploits the sparse and symmetric structure of the Hessian matrix and avoids the need for direct matrix inversion. This approach shifts the computation from realm of linear algebra to that of probabilistic inference on graphical models, thus applying GaBP as an efficient inference engine. Our construction is general and can be used for any interior-point algorithm which uses the Newton method, including non-linear program solvers.

cs.IT↗

arXiv2008

Gaussian Belief Propagation Solver for Systems of Linear Equations

The canonical problem of solving a system of linear equations arises in numerous contexts in information theory, communication theory, and related fields. In this contribution, we develop a solution based upon Gaussian belief propagation (GaBP) that does not involve direct matrix inversion. The iterative nature of our approach allows for a distributed message-passing implementation of the solution algorithm. We also address some properties of the GaBP solver, including convergence, exactness, its max-product version and relation to classical solution methods. The application example of decorrelation in CDMA is used to demonstrate the faster convergence rate of the proposed solver in comparison to conventional linear-algebraic iterative solution methods.

cs.IT↗

arXiv2008

Gaussian Belief Propagation Based Multiuser Detection

In this work, we present a novel construction for solving the linear multiuser detection problem using the Gaussian Belief Propagation algorithm. Our algorithm yields an efficient, iterative and distributed implementation of the MMSE detector. We compare our algorithm's performance to a recent result and show an improved memory consumption, reduced computation steps and a reduction in the number of sent messages. We prove that recent work by Montanari et al. is an instance of our general algorithm, providing new convergence results for both algorithms.

cs.IT↗

arXiv2008

Gaussian Belief Propagation for Solving Systems of Linear Equations: Theory and Application

The canonical problem of solving a system of linear equations arises in numerous contexts in information theory, communication theory, and related fields. In this contribution, we develop a solution based upon Gaussian belief propagation (GaBP) that does not involve direct matrix inversion. The iterative nature of our approach allows for a distributed message-passing implementation of the solution algorithm. We address the properties of the GaBP solver, including convergence, exactness, computational complexity, message-passing efficiency and its relation to classical solution methods. We use numerical examples and applications, like linear detection, to illustrate these properties through the use of computer simulations. This empirical study demonstrates the attractiveness (e.g., faster convergence rate) of the proposed GaBP solver in comparison to conventional linear-algebraic iterative solution methods.

cs.IT↗

arXiv2008

Carnot in the Information Age: Discrete Symmetric Channels

Modeling communication channels as thermal systems results in Hamiltonians which are an explicit function of the temperature. The first two authors have recently generalized the second thermodynamic law to encompass systems with temperature-dependent energy levels, $dQ=TdS+ dT$, where {$<\cdot>$} denotes averaging over the Boltzmann distribution, recomputing the mutual information and other main properties of the popular Gaussian channel. Here the mutual information for the binary symmetric channel as well as for the discrete symmetric channel consisting of 4 input/output (I/O) symbols is explicitly calculated using the generalized second law of thermodynamics. For equiprobable I/O the mutual information of the examined channels has a very simple form, -$γU(γ)|_0^β$, where $U$ denotes the internal energy of the channel. We prove that this simple form of the mutual information governs the class of discrete memoryless symmetric communication channels with equiprobable I/O symbols.

cond-mat.stat-mech↗

arXiv2008

Shannon Meets Carnot: Generalized Second Thermodynamic Law

The classical thermodynamic laws fail to capture the behavior of systems with energy Hamiltonian which is an explicit function of the temperature. Such Hamiltonian arises, for example, in modeling information processing systems, like communication channels, as thermal systems. Here we generalize the second thermodynamic law to encompass systems with temperature-dependent energy levels, $dQ=TdS+ dT$, where $<\cdot>$ denotes averaging over the Boltzmann distribution and reveal a new definition to the basic notion of temperature. This generalization enables to express, for instance, the mutual information of the Gaussian channel as a consequence of the fundamental laws of nature - the laws of thermodynamics.

cond-mat.stat-mech↗