arXiv subjects

Gregory W. Wornell

Publications and source records attributed to Gregory W. Wornell.

At least 55 records · Page 3Linked to original sources

arXiv2021

Blind Modulo Analog-to-Digital Conversion

In a growing number of applications, there is a need to digitize signals whose spectral characteristics are challenging for traditional Analog-to-Digital Converters (ADCs). Examples, among others, include systems where the ADC must acquire at once a very wide but sparsely and dynamically occupied bandwidth supporting diverse services, as well as systems where the signal of interest is subject to strong narrowband co-channel interference. In such scenarios, the resolution requirements can be prohibitively high. As an alternative, the recently proposed modulo-ADC architecture can in principle require dramatically fewer bits in the conversation to obtain the target fidelity, but requires that information about the spectrum be known and explicitly taken into account by the analog and digital processing in the converter, which is frequently impractical. To address this limitation, we develop a blind version of the architecture that requires no such knowledge in the converter, without sacrificing performance. In particular, it features an automatic modulo-level adjustment and a fully adaptive modulo unwrapping mechanism, allowing it to asymptotically match the characteristics of the unknown input signal. In addition to detailed analysis, simulations demonstrate the attractive performance characteristics in representative settings.

eess.SP↗

arXiv2021

One-Bit Direct Position Determination of Narrowband Gaussian Signals

One of the main drawbacks of the well-known Direct Position Determination (DPD) method is the requirement that raw signal data be transferred to a common processor. It would therefore be of high practical value if DPD$-$or a modified version thereof$-$could be successfully applied to a coarsely quantized version of the raw data, thus alleviating the requirements on the communication links between the different base stations. Motivated by the above, and inspired by recent work in the rejuvenated one-bit array processing field, we present One-Bit DPD: a method for direct localization based on one-bit quantized measurements. We show that despite the coarse quantization, the proposed method nonetheless yields an estimate for the unknown emitter position with appealing asymptotic properties. We further establish the underlying identifiability conditions of this model, which rely only on second-order statistics. Empirical simulation results corroborate our analytical derivations, demonstrating that much of the information regarding the unknown emitter position is preserved under this crude form of quantization.

eess.SP↗

arXiv2020

On Learning Continuous Pairwise Markov Random Fields

We consider learning a sparse pairwise Markov Random Field (MRF) with continuous-valued variables from i.i.d samples. We adapt the algorithm of Vuffray et al. (2019) to this setting and provide finite-sample analysis revealing sample complexity scaling logarithmically with the number of variables, as in the discrete and Gaussian settings. Our approach is applicable to a large class of pairwise MRFs with continuous variables and also has desirable asymptotic properties, including consistency and normality under mild conditions. Further, we establish that the population version of the optimization criterion employed in Vuffray et al. (2019) can be interpreted as local maximum likelihood estimation (MLE). As part of our analysis, we introduce a robust variation of sparse linear regression a` la Lasso, which may be of interest in its own right.

cs.LG↗

arXiv2020

Bregman Divergence Bounds and Universality Properties of the Logarithmic Loss

A loss function measures the discrepancy between the true values and their estimated fits, for a given instance of data. In classification problems, a loss function is said to be proper if a minimizer of the expected loss is the true underlying probability. We show that for binary classification, the divergence associated with smooth, proper, and convex loss functions is upper bounded by the Kullback-Leibler (KL) divergence, to within a normalization constant. This implies that by minimizing the logarithmic loss associated with the KL divergence, we minimize an upper bound to any choice of loss from this set. As such the logarithmic loss is universal in the sense of providing performance guarantees with respect to a broad class of accuracy measures. Importantly, this notion of universality is not problem-specific, enabling its use in diverse applications, including predictive modeling, data clustering and sample complexity analysis. Generalizations to arbitrary finite alphabets are also developed. The derived inequalities extend several well-known $f$-divergence results.

cs.IT↗

arXiv2019

Computational Mirrors: Blind Inverse Light Transport by Deep Matrix Factorization

We recover a video of the motion taking place in a hidden scene by observing changes in indirect illumination in a nearby uncalibrated visible region. We solve this problem by factoring the observed video into a matrix product between the unknown hidden scene video and an unknown light transport matrix. This task is extremely ill-posed, as any non-negative factorization will satisfy the data. Inspired by recent work on the Deep Image Prior, we parameterize the factor matrices using randomly initialized convolutional neural networks trained in a one-off manner, and show that this results in decompositions that reflect the true motion in the hidden scene.

cs.CV↗

arXiv2019

On Universal Features for High-Dimensional Learning and Inference

We consider the problem of identifying universal low-dimensional features from high-dimensional data for inference tasks in settings involving learning. For such problems, we introduce natural notions of universality and we show a local equivalence among them. Our analysis is naturally expressed via information geometry, and represents a conceptually and computationally useful analysis. The development reveals the complementary roles of the singular value decomposition, Hirschfeld-Gebelein-Rényi maximal correlation, the canonical correlation and principle component analyses of Hotelling and Pearson, Tishby's information bottleneck, Wyner's common information, Ky Fan $k$-norms, and Brieman and Friedman's alternating conditional expectations algorithm. We further illustrate how this framework facilitates understanding and optimizing aspects of learning systems, including multinomial logistic (softmax) regression and the associated neural network architecture, matrix factorization methods for collaborative filtering and other applications, rank-constrained multivariate linear regression, and forms of semi-supervised learning.

cs.LG↗

arXiv2019

Super-Nyquist Rateless Coding for Intersymbol Interference Channels

A rateless transmission architecture is developed for communication over Gaussian intersymbol interference channels, based on the concept of super-Nyquist (SNQ) signaling. In such systems, the signaling rate is chosen significantly higher than the Nyquist rate of the system. We show that such signaling, when used in conjunction with good "off-the-shelf" base codes, simple linear redundancy, and minimum mean-square error decision feedback equalization, results in capacity-approaching, low-complexity rateless codes for the time-varying intersymbol-interference channel. Constructions for both single-input / single-output (SISO) and multi-input / multi-output (MIMO) ISI channels are developed.

cs.IT↗

arXiv2019

An Information Theoretic Interpretation to Deep Neural Networks

It is commonly believed that the hidden layers of deep neural networks (DNNs) attempt to extract informative features for learning tasks. In this paper, we formalize this intuition by showing that the features extracted by DNN coincide with the result of an optimization problem, which we call the `universal feature selection' problem, in a local analysis regime. We interpret the weights training in DNN as the projection of feature functions between feature spaces, specified by the network structure. Our formulation has direct operational meaning in terms of the performance for inference tasks, and gives interpretations to the internal computation results of DNNs. Results of numerical experiments are provided to support the analysis.

cs.IT↗

arXiv2018

A Modulo-Based Architecture for Analog-to-Digital Conversion

Systems that capture and process analog signals must first acquire them through an analog-to-digital converter. While subsequent digital processing can remove statistical correlations present in the acquired data, the dynamic range of the converter is typically scaled to match that of the input analog signal. The present paper develops an approach for analog-to-digital conversion that aims at minimizing the number of bits per sample at the output of the converter. This is attained by reducing the dynamic range of the analog signal by performing a modulo operation on its amplitude, and then quantizing the result. While the converter itself is universal and agnostic of the statistics of the signal, the decoder operation on the output of the quantizer can exploit the statistical structure in order to unwrap the modulo folding. The performance of this method is shown to approach information theoretical limits, as captured by the rate-distortion function, in various settings. An architecture for modulo analog-to-digital conversion via ring oscillators is suggested, and its merits are numerically demonstrated.

cs.IT↗

arXiv2018

On the Universality of the Logistic Loss Function

A loss function measures the discrepancy between the true values (observations) and their estimated fits, for a given instance of data. A loss function is said to be proper (unbiased, Fisher consistent) if the fits are defined over a unit simplex, and the minimizer of the expected loss is the true underlying probability of the data. Typical examples are the zero-one loss, the quadratic loss and the Bernoulli log-likelihood loss (log-loss). In this work we show that for binary classification problems, the divergence associated with smooth, proper and convex loss functions is bounded from above by the Kullback-Leibler (KL) divergence, up to a multiplicative normalization constant. It implies that by minimizing the log-loss (associated with the KL divergence), we minimize an upper bound to any choice of loss functions from this set. This property justifies the broad use of log-loss in regression, decision trees, deep neural networks and many other applications. In addition, we show that the KL divergence bounds from above any separable Bregman divergence that is convex in its second argument (up to a multiplicative normalization constant). This result introduces a new set of divergence inequalities, similar to the well-known Pinsker inequality.

cs.IT↗

arXiv2018

Revealing hidden scenes by photon-efficient occlusion-based opportunistic active imaging

The ability to see around corners, i.e., recover details of a hidden scene from its reflections in the surrounding environment, is of considerable interest in a wide range of applications. However, the diffuse nature of light reflected from typical surfaces leads to mixing of spatial information in the collected light, precluding useful scene reconstruction. Here, we employ a computational imaging technique that opportunistically exploits the presence of occluding objects, which obstruct probe-light propagation in the hidden scene, to undo the mixing and greatly improve scene recovery. Importantly, our technique obviates the need for the ultrafast time-of-flight measurements employed by most previous approaches to hidden-scene imaging. Moreover, it does so in a photon-efficient manner based on an accurate forward model and a computational algorithm that, together, respect the physics of three-bounce light propagation and single-photon detection. Using our methodology, we demonstrate reconstruction of hidden-surface reflectivity patterns in a meter-scale environment from non-time-resolved measurements. Ultimately, our technique represents an instance of a rich and promising new imaging modality with important potential implications for imaging science.

stat.AP↗

arXiv2017

Sensor Array Design Through Submodular Optimization

We consider the problem of far-field sensing by means of a sensor array. Traditional array geometry design techniques are agnostic to prior information about the far-field scene. However, in many applications such priors are available and may be utilized to design more efficient array topologies. We formulate the problem of array geometry design with scene prior as one of finding a sampling configuration that enables efficient inference, which turns out to be a combinatorial optimization problem. While generic combinatorial optimization problems are NP-hard and resist efficient solvers, we show how for array design problems the theory of submodular optimization may be utilized to obtain efficient algorithms that are guaranteed to achieve solutions within a constant approximation factor from the optimum. We leverage the connection between array design problems and submodular optimization and port several results of interest. We demonstrate efficient methods for designing arrays with constraints on the sensing aperture, as well as arrays respecting combinatorial placement constraints. This novel connection between array design and submodularity suggests the possibility for utilizing other insights and techniques from the growing body of literature on submodular optimization in the field of array design.

cs.IT↗

arXiv2017

Exploiting Occlusion in Non-Line-of-Sight Active Imaging

Active non-line-of-sight imaging systems are of growing interest for diverse applications. The most commonly proposed approaches to date rely on exploiting time-resolved measurements, i.e., measuring the time it takes for short light pulses to transit the scene. This typically requires expensive, specialized, ultrafast lasers and detectors that must be carefully calibrated. We develop an alternative approach that exploits the valuable role that natural occluders in a scene play in enabling accurate and practical image formation in such settings without such hardware complexity. In particular, we demonstrate that the presence of occluders in the hidden scene can obviate the need for collecting time-resolved measurements, and develop an accompanying analysis for such systems and their generalizations. Ultimately, the results suggest the potential to develop increasingly sophisticated future systems that are able to identify and exploit diverse structural features of the environment to reconstruct scenes hidden from view.

eess.IV↗

arXiv2017

Covert Communication with Channel-State Information at the Transmitter

We consider the problem of covert communication over a state-dependent channel, where the transmitter has causal or noncausal knowledge of the channel states. Here, "covert" means that a warden on the channel should observe similar statistics when the transmitter is sending a message and when it is not. When a sufficiently long secret key is shared between the transmitter and the receiver, we derive closed-form formulas for the maximum achievable covert communication rate ("covert capacity") for discrete memoryless channels and, when the transmitter's channel-state information (CSI) is noncausal, for additive white Gaussian noise (AWGN) channels. For certain channel models, including the AWGN channel, we show that the covert capacity is positive with CSI at the transmitter, but is zero without CSI. We also derive lower bounds on the rate of the secret key that is needed for the transmitter and the receiver to achieve the covert capacity.

cs.IT↗

arXiv2015

Photon-efficient quantum cryptography with pulse-position modulation

The binary (one-bit-per-photon) encoding that most existing quantum key distribution (QKD) protocols employ puts a fundamental limit on their achievable key rates, especially under high channel loss conditions associated with long-distance fiber-optic or satellite-to-ground links. Inspired by the pulse-position-modulation (PPM) approach to photon-starved classical communications, we design and demonstrate the first PPM-QKD, whose security against collective attacks is established through continuous-variable entanglement measurements that also enable a novel decoy-state protocol performed conveniently in post processing. We achieve a throughput of 8.0 Mbit/s (2.5 Mbit/s for loss equivalent to 25 km of fiber) and secret-key capacity up to 4.0 bits per detected photon, thus demonstrating the significant enhancement afforded by high-dimensional encoding. These results point to a new avenue for realizing high-throughput satellite-based or long-haul fiber-optic quantum communications beyond their photon-reception-rate limits.

quant-ph↗

arXiv2014

Toward Photon-Efficient Key Distribution over Optical Channels

This work considers the distribution of a secret key over an optical (bosonic) channel in the regime of high photon efficiency, i.e., when the number of secret key bits generated per detected photon is high. While in principle the photon efficiency is unbounded, there is an inherent tradeoff between this efficiency and the key generation rate (with respect to the channel bandwidth). We derive asymptotic expressions for the optimal generation rates in the photon-efficient limit, and propose schemes that approach these limits up to certain approximations. The schemes are practical, in the sense that they use coherent or temporally-entangled optical states and direct photodetection, all of which are reasonably easy to realize in practice, in conjunction with off-the-shelf classical codes.

cs.IT↗

arXiv2014

A refined analysis of the Poisson channel in the high-photon-efficiency regime

We study the discrete-time Poisson channel under the constraint that its average input power (in photons per channel use) must not exceed some constant E. We consider the wideband, high-photon-efficiency extreme where E approaches zero, and where the channel's "dark current" approaches zero proportionally with E. Improving over a previously obtained first-order capacity approximation, we derive a refined approximation, which includes the exact characterization of the second-order term, as well as an asymptotic characterization of the third-order term with respect to the dark current. We also show that pulse-position modulation is nearly optimal in this regime.

cs.IT↗

arXiv2013

Update-Efficiency and Local Repairability Limits for Capacity Approaching Codes

Motivated by distributed storage applications, we investigate the degree to which capacity achieving encodings can be efficiently updated when a single information bit changes, and the degree to which such encodings can be efficiently (i.e., locally) repaired when single encoded bit is lost. Specifically, we first develop conditions under which optimum error-correction and update-efficiency are possible, and establish that the number of encoded bits that must change in response to a change in a single information bit must scale logarithmically in the block-length of the code if we are to achieve any nontrivial rate with vanishing probability of error over the binary erasure or binary symmetric channels. Moreover, we show there exist capacity-achieving codes with this scaling. With respect to local repairability, we develop tight upper and lower bounds on the number of remaining encoded bits that are needed to recover a single lost bit of the encoding. In particular, we show that if the code-rate is $ε$ less than the capacity, then for optimal codes, the maximum number of codeword symbols required to recover one lost symbol must scale as $\log1/ε$. Several variations on---and extensions of---these results are also developed.

cs.IT↗