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The papers in this special section focuses on signal processing advances in wireless transmission of power and information. Wireless power transfer (WPT) and wireless information and power transfer (WIPT) have received growing attention in the research community in the past few years. In this special issue, a total of fourteen papers present state-of-the-art results in the broad area of wireless transmission of information and power with a special emphasis on signal processing advances. The special issue starts with a guest editor-authored tutorial overview paper that reviews the signal processing, machine learning, sensing, and computing techniques, challenges and opportunities in future networks based on WPT and WIPT.

The CEO problem has received much attention since first introduced by Berger et al ., but there are limited results on non-Gaussian models with non-quadratic distortion measures. In this work, we extend the quadratic Gaussian CEO problem to two non-Gaussian settings with general $r$ th power of difference distortion. Assuming an identical observation channel across agents, we study the asymptotics of distortion decay as the number of agents and sum-rate, $R_{\textsf {sum}}$ , grow without bound, while individual rates vanish. The first setting is a regular source-observation model with $r$ th power of difference distortion, which subsumes the quadratic Gaussian CEO problem, and we establish that the distortion decays at $\mathcal {O}(R_{\textsf {sum}}^{-r/2})$ when $r \ge 2$ . We use sample median estimation after the Berger-Tung scheme for achievability. The other setting is a non-regular source-observation model, including uniform additive noise models, with $r$ th power of difference distortion for which estimation-theoretic regularity conditions do not hold. The distortion decay $\mathcal {O}(R_{\textsf {sum}}^{-r})$ when $r \ge 1$ is obtained for the non-regular model by midrange estimator following the Berger-Tung scheme. We also provide converses based on the Shannon lower bound for the regular model and the Chazan-Zakai-Ziv bound for the non-regular model, respectively. Lastly, we provide a sufficient condition for the regular model, under which quadratic and logarithmic distortions are asymptotically equivalent by an entropy power relationship as the number of agents grows. This proof relies on the Bernstein-von Mises theorem.

The “bee-identification problem” was formally defined by Tandon, Tan and Varshney [ IEEE Trans. Commun. , vol. 67, 2019], and the error exponent was studied. This work extends the results for the “absentee bees” scenario, where a fraction of the bees are absent in the beehive image used for identification. For this setting, we present an exact characterization of the bee-identification error exponent, and show that independent barcode decoding is optimal, i.e., joint decoding of the bee barcodes does not result in a better error exponent relative to independent decoding of each noisy barcode. This is in contrast to the result without absentee bees, where joint barcode decoding results in a significantly higher error exponent than independent barcode decoding. We also define and characterize the ‘capacity’ for the bee-identification problem with absentee bees, and prove a strong converse for the same.

Neurobiological systems operate at power levels that are unattainable by modern electronic systems while exhibiting broader information processing capabilities for a number of important tasks. A variety of engineered systems designed for energy efficiency or hardware simplicity use time-based signal representations, which share similar mathematical principles with those that arise naturally in biology. In general, time-based signal representations refer to embedding information into the timing, density, or duration of a predetermined, and often bipolar, waveform. In mammalian nervous systems, it is generally accepted that neurons embed information into the timing and firing density of the sudden changes in their membrane potential, or spikes. Similarly, many low-power electronic systems use signal representations that embed information in the timing, repetition frequency, or duration of simple pulse waveforms. Despite their apparent similarities, such signal representations are often studied in different contexts.

Consider the problem of identifying a massive number of bees, uniquely labeled with barcodes, using noisy measurements. We formally introduce this “bee-identification problem”, define its error exponent, and derive efficiently computable upper and lower bounds for this exponent. We show that joint decoding of barcodes provides a significantly better exponent compared to separate decoding followed by permutation inference. For low rates, we prove that the lower bound on the bee-identification exponent obtained using typical random codes (TRC) is strictly better than the corresponding bound obtained using a random code ensemble (RCE). Further, as the rate approaches zero, we prove that the upper bound on the bee-identification exponent meets the lower bound obtained using TRC with joint barcode decoding.

This work explores a social learning problem with agents having nonidentical noise variances and mismatched beliefs. We consider an $N$-agent binary hypothesis test in which each agent sequentially makes a decision based not only on a private observation, but also on preceding agents' decisions. In addition, the agents have their own beliefs instead of the true prior, and have nonidentical noise variances in the private signal. We focus on the Bayes risk of the last agent, where preceding agents are selfish. We first derive the optimal decision rule by recursive belief update and conclude, counterintuitively, that beliefs deviating from the true prior could be optimal in this setting. The effect of nonidentical noise levels in the two-agent case is also considered and analytical properties of the optimal belief curves are given. Next, we consider a predecessor selection problem wherein the subsequent agent of a certain belief chooses a predecessor from a set of candidates with varying beliefs. We characterize the decision region for choosing such a predecessor and argue that a subsequent agent with beliefs varying from the true prior often ends up selecting a suboptimal predecessor, indicating the need for a social planner. Lastly, we discuss an augmented intelligence design problem that uses a model of human behavior from cumulative prospect theory and investigate its near-optimality and suboptimality., final version, to appear in IEEE Transactions on Signal Processing

This paper considers the problem of simultaneous information and energy transmission, where the energy harvesting function is only known experimentally at sample points, e.g., due to nonlinearities and parameter uncertainties in harvesting circuits. We investigate the performance loss due to this partial knowledge of the harvesting function in terms of transmitted energy and information. In particular, we assume that the harvesting function is a subclass of the Sobolev space and consider two cases, where the experimental samples are either taken noiselessly or in the presence of noise. Using constructive function approximation and regression methods for noiseless and noisy samples, respectively, we show that the worst loss in energy transmission vanishes asymptotically as the number of samples increase. Similarly, the loss in information rate vanishes in the interior of the energy domain; however, it does not always vanish at maximal energy. We further show that the same principle applies in multicast settings, such as medium access in the Wi-Fi protocol. We also consider the end-to-end source–channel communication problem under source distortion constraint and channel energy requirement, where both distortion and harvesting functions are known only at samples.

In a recent essay on the role of modern information technologies in democratic processes, Zeynep Tufekci described the actions of Egyptian leader Hosni Mubarak in cutting off Internet and cellular service during the 2011 Tahrir uprising as follows: "The move backfired: it restricted the flow of information coming out of Tahrir Square but caused international attention on Egypt to spike. He hadn't understood that in the 21st century it is the flow of attention, not information (which we already have too much of), that matters."

Blockchain systems store transaction data in the form of a distributed ledger where each peer is to maintain an identical copy. Blockchain systems resemble repetition codes, incurring high storage cost. Recently, distributed storage blockchain (DSB) systems have been proposed to improve storage efficiency by incorporating secret sharing, private key encryption, and information dispersal algorithms. However, the DSB results in significant communication cost when peer failures occur due to denial of service attacks. In this letter, we propose a new DSB approach based on a local secret sharing (LSS) scheme with a hierarchical secret structure of one global secret and several local secrets. The proposed DSB approach with LSS improves the storage and recovery communication costs.

We consider the problem of universal joint clustering and registration of images. Image clustering focuses on grouping similar images, while image registration refers to the task of aligning copies of an image that have been subject to rigid-body transformations, such as rotations and translations. We first study registering two images using maximum mutual information and prove its asymptotic optimality. We then show the shortcomings of pairwise registration in multi-image registration, and design an asymptotically optimal algorithm based on multi-information. Further, we define a novel multivariate information functional to perform joint clustering and registration of images, and prove consistency of the algorithm. Finally, we consider registration and clustering of numerous limited-resolution images, defining algorithms that are order-optimal in scaling of number of pixels in each image with the number of images.

With the advent of the Internet of Things (IoT) and a rapid deployment of smart devices and wireless sensor networks (WSNs), humans interact extensively with machine data. These human decision makers use sensors that provide information through a sociotechnical network. The sensors can be other human users or they can be IoT devices. The decision makers themselves are also part of the network, and there is a need to understand how they will behave. In this paper, the decision fusion behavior of humans is analyzed on the basis of behavioral experiments. The data collected from these experiments demonstrate that people perform decision fusion in a stochastic manner dependent on various factors, unlike machines that perform this task in a deterministic manner. A Bayesian hierarchical model is developed to characterize the observed stochastic human behavior. This hierarchical model captures the differences observed in people at individual, crowd, and population levels. The implications of such a model on designing large-scale inference systems are presented by developing optimal decision fusion trees with both human and machine agents.

Crowdsourcing of jobs to online freelance platforms is rapidly gaining popularity. Most crowdsourcing platforms are uncontrolled and offer freedom to customers and freelancers to choose each other. This works well for unskilled jobs (e.g., image classification) with no specific quality requirement since freelancers are functionally identical. For skilled jobs (e.g., software development) with specific quality requirements, however, this does not ensure that the maximum number of job requests is satisfied. In this paper, we determine the capacity of regulated freelance systems, in terms of maximum satisfied job requests, and propose centralized schemes that achieve capacity. To ensure decentralized operation and freedom for customers and freelancers, we propose simple schemes compatible with the operation of current crowdsourcing platforms that approximately achieve capacity. Furthermore, for settings where the number of job requests exceeds capacity, we propose a scheme that is agnostic of that information, but is optimal and fair in declining jobs without wait.

We study how to optimally attract new customers using a referral program. Whenever a consumer makes a purchase, the firm gives her a link to share with friends, and every purchase coming through that link generates a referral payment. The firm chooses the referral payment function and consumers play an equilibrium in response. The optimal payment function is nonlinear and not necessarily monotonic in the number of successful referrals. If we approximate the optimal policy using a linear payment function, the approximation loss scales with the square root of the average consumer degree. Using a threshold payment, the approximation loss scales proportionally to the average consumer degree. Combining the two, using a linear payment function with a threshold bonus, we can achieve a constant bound on the approximation loss. This paper was accepted by Noah Gans, stochastic models and simulation.

In software-as-a-service applications provisioned through cloud computing, locally cached data are often modified with updates from new versions. In some cases, with each edit, one may want to preserve both the original and new versions. In this paper, we focus on cases in which only the latest version must be preserved. Furthermore, it is desirable for the data to not only be compressed but to also be easily modified during updates, since representing information and modifying the representation both incur cost. We examine whether it is possible to have both compression efficiency and ease of alteration, in order to promote codeword reuse. In other words, we study the feasibility of a malleable and efficient coding scheme. The tradeoff between compression efficiency and malleability cost—the difficulty of synchronizing compressed versions—is measured as the length of a reused prefix portion. The region of achievable rates and malleability is found. Drawing from prior work on common information problems, we show that efficient data compression may not be the best engineering design principle when storing software-as-a-service data. In the general case, goals of efficiency and malleability are fundamentally in conflict.

Recent advances in associative memory design through structured pattern sets and graph-based inference algorithms have allowed reliable learning and recall of an exponential number of patterns. Although these designs correct external errors in recall, they assume neurons that compute noiselessly, in contrast to the highly variable neurons in brain regions thought to operate associatively such as hippocampus and olfactory cortex. Here we consider associative memories with noisy internal computations and analytically characterize performance. As long as the internal noise level is below a specified threshold, the error probability in the recall phase can be made exceedingly small. More surprisingly, we show that internal noise actually improves the performance of the recall phase while the pattern retrieval capacity remains intact, i.e., the number of stored patterns does not reduce with noise (up to a threshold). Computational experiments lend additional support to our theoretical analysis. This work suggests a functional benefit to noisy neurons in biological neuronal networks., Comment: arXiv admin note: text overlap with arXiv:1301.6265

The wiring economy principle in neuroscience has explained many experimentally observed properties of neuronal networks by asserting the need to keep the axons and dendrites that connect neurons small in length. Just like neuronal networks, many distributed systems are physical constructs that incur deployment and maintenance costs for their communication infrastructure. Taking wiring economy as a design goal for engineering systems that perform distributed coordination and inference, this paper formulates and studies the tradeoff between performance and wiring cost. It is shown that separated communication topology design and physical node placement yields optimal design. Designing optimal networks is shown to be NP-complete. The natural relaxation to the integer network design problem is shown to be a reverse convex program. Small optimal networks are computed. Optimally placed random network topologies are demonstrated to have good performance.

Given the possibility of communication systems failing catastrophically, we investigate limits to communicating over channels that fail at random times. These channels are finite-state semi-Markov channels. We show that communication with arbitrarily small probability of error is not possible. Making use of results in finite blocklength channel coding, we determine sequences of blocklengths that optimize transmission volume communicated at fixed maximum message error probabilities. We provide a partial ordering of communication channels. A dynamic programming formulation is used to show the structural result that channel state feedback does not improve performance.

Departing from traditional communication theory where decoding algorithms are assumed to perform without error, a system where noise perturbs both computational devices and communication channels is considered here. This paper studies limits in processing noisy signals with noisy circuits by investigating the effect of noise on standard iterative decoders for low-density parity-check codes. Concentration of decoding performance around its average is shown to hold when noise is introduced into message-passing and local computation. Density evolution equations for simple faulty iterative decoders are derived. In one model, computing nonlinear estimation thresholds shows that performance degrades smoothly as decoder noise increases, but arbitrarily small probability of error is not achievable. Probability of error may be driven to zero in another system model; the decoding threshold again decreases smoothly with decoder noise. As an application of the methods developed, an achievability result for reliable memory systems constructed from unreliable components is provided., Revised in May 2010 in response to reviewer comments

Permutation codes are a class of structured vector quantizers with a computationally-simple encoding procedure based on sorting the scalar components. Using a codebook comprising several permutation codes as subcodes preserves the simplicity of encoding while increasing the number of rate-distortion operating points, improving the convex hull of operating points, and increasing design complexity. We show that when the subcodes are designed with the same composition, optimization of the codebook reduces to a lower-dimensional vector quantizer design within a single cone. Heuristics for reducing design complexity are presented, including an optimization of the rate allocation in a shape-gain vector quantizer with gain-dependent wrapped spherical shape codebook.

SummaryExperimental investigations have revealed that synapses possess interesting and, in some cases, unexpected properties. We propose a theoretical framework that accounts for three of these properties: typical central synapses are noisy, the distribution of synaptic weights among central synapses is wide, and synaptic connectivity between neurons is sparse. We also comment on the possibility that synaptic weights may vary in discrete steps. Our approach is based on maximizing information storage capacity of neural tissue under resource constraints. Based on previous experimental and theoretical work, we use volume as a limited resource and utilize the empirical relationship between volume and synaptic weight. Solutions of our constrained optimization problems are not only consistent with existing experimental measurements but also make nontrivial predictions.

It is well known that uncoded transmission of a memoryless Gaussian source over a memoryless additive white Gaussian noise channel results in optimal performance theoretically attainable. When there is additional interference in the channel, uncoded transmission is robust. It achieves the same sensitivity performance as optimal performance, measured using sensitivity results of Pinsker, Prelov, and Verdu.