arXiv subjects

Michele Wigger

Publications and source records attributed to Michele Wigger.

At least 19 recordsLinked to original sources

arXiv2023

Strong Converses for Memoryless Bi-Static ISAC

The paper characterizes the fundamental limits of integrated sensing and communication (ISAC) systems with a bi-static radar, where the radar receiver is located close to the transmitter and estimates or detects the state based on the transmitter's channel inputs and the backscattered signals. Two models are considered. In the first model, the memoryless state sequence is distributed according to a fixed distribution and the goal of the radar receiver is to reconstruct this state-sequence with smallest possible distortion. In the second model, the memoryless state is distributed either according to $P_S$ or to $Q_S$ and the radar's goal is to detect this underlying distribution so that the missed-detection error probability has maximum exponential decay-rate (maximum Stein exponent). Similarly to previous results, our fundamental limits show that the tradeoff between sensing and communication solely stems from the empirical statistics of the transmitted codewords which influences both performances. The main technical contribution are two strong converse proofs that hold for all probabilities of communication error $ε$ and excess-distortion probability or false-alarm probability $δ$ summing to less than 1, $ε+δ< 1$. These proofs are based on two parallel change-of-measure arguments on the sets of typical sequences, one change-of-measure to obtain the desired bound on the communication rate, and the second to bound the sensing performance.

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arXiv2023

Strong Converses using Typical Changes of Measures and Asymptotic Markov Chains

The paper presents exponentially-strong converses for source-coding, channel coding, and hypothesis testing problems. More specifically, it presents alternative proofs for the well-known exponentially-strong converse bounds for almost lossless source-coding with side-information and for channel coding over a discrete memoryless channel (DMC). These alternative proofs are solely based on a change of measure argument on the sets of conditionally or jointly typical sequences that result in a correct decision, and on the analysis of these measures in the asymptotic regime of infinite blocklengths. The paper also presents a new exponentially-strong converse for the K-hop hypothesis testing against independence problem with certain Markov chains and a strong converse for the two-terminal Lround interactive compression problem with multiple distortion constraints that depend on both sources and both reconstructions. This latter problem includes as special cases the Wyner-Ziv problem, the interactive function computation problem, and the compression with lossy common reconstruction problem. These new strong converse proofs are derived using similar change of measure arguments as described above and by additionally proving that certain Markov chains involving auxiliary random variables hold in the asymptotic regime of infinite blocklengths. As shown in related publications, the same method also yields converse bounds under expected resource constraints.

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arXiv2022

Testing Against Independence with an Eavesdropper

We study a distributed binary hypothesis testing (HT) problem with communication and security constraints, involving three parties: a remote sensor called Alice, a legitimate decision centre called Bob, and an eavesdropper called Eve, all having their own source observations. In this system, Alice conveys a rate R description of her observation to Bob, and Bob performs a binary hypothesis test on the joint distribution underlying his and Alice's observations. The goal of Alice and Bob is to maximise the exponential decay of Bob's miss-detection (type II-error) probability under two constraints: Bob's false alarm-probability (type-I error) probability has to stay below a given threshold and Eve's uncertainty (equivocation) about Alice's observations should stay above a given security threshold even when Eve learns Alice's message. For the special case of testing against independence, we characterise the largest possible type-II error exponent under the described type-I error probability and security constraints.

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arXiv2022

Coding for Sensing: An Improved Scheme for Integrated Sensing and Communication over MACs

A memoryless state-dependent multiple-access channel (MAC) is considered, where two transmitters wish to convey their messages to a single receiver while simultaneously sensing (estimating) the respective states via generalized feedbacks. For this channel, an improved inner bound is provided on the fundamental rate-distortions tradeoff which characterizes the communication rates the transmitters can achieve while simultaneously ensuring that their state-estimates satisfy desired distortion criteria. The new inner bound is based on a scheme where each transmitter codes over the generalized feedback so as to improve the state estimation at the other transmitter. This is in contrast to the schemes proposed for point-to-point and broadcast channels where coding is used only for the transmission of messages and the optimal estimators operate on a symbol-by-symbol basis on the sequences of channel inputs and feedback outputs.

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arXiv2021

Cache Updating Strategy Minimizing the Age of Information with Time-Varying Files' Popularities

We consider updating strategies for a local cache which downloads time-sensitive files from a remote server through a bandwidth-constrained link. The files are requested randomly from the cache by local users according to a popularity distribution which varies over time according to a Markov chain structure. We measure the freshness of the requested time-sensitive files through their Age of Information (AoI). The goal is then to minimize the average AoI of all requested files by appropriately designing the local cache's downloading strategy. To achieve this goal, the original problem is relaxed and cast into a Constrained Markov Decision Problem (CMDP), which we solve using a Lagrangian approach and Linear Programming. Inspired by this solution for the relaxed problem, we propose a practical cache updating strategy that meets all the constraints of the original problem. Under certain assumptions, the practical updating strategy is shown to be optimal for the original problem in the asymptotic regime of a large number of files. For a finite number of files, we show the gain of our practical updating strategy over the traditional square-root-law strategy (which is optimal for fixed non time-varying file popularities) through numerical simulations.

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arXiv2020

Coordinated Multi Point Transmission and Reception for Mixed-Delay Traffic

This paper analyzes the multiplexing gains (MG) for simultaneous transmission of delay-sensitive and delay-tolerant data over interference networks. In the considered model, only delay-tolerant data can profit from coordinated multipoint (CoMP) transmission or reception techniques, because delay-sensitive data has to be transmitted without further delay. Transmission of delay-tolerant data is also subject to a delay constraint, which is however less stringent than the one on delay-sensitive data. Different coding schemes are proposed, and the corresponding MG pairs for delay-sensitive and delay-tolerant data are characterized for Wyner's linear symmetric network and for Wyner's two-dimensional hexagonal network with and without sectorization. For Wyner's linear symmetric also an information-theoretic converse is established and shown to be exact whenever the cooperation rates are sufficiently large or the delay-sensitive MG is small or moderate. These results show that on Wyner's symmetric linear network and for sufficiently large cooperation rates, the largest MG for delay-sensitive data can be achieved without penalizing the maximum sum-MG of both delay-sensitive and delay-tolerant data. A similar conclusion holds for Wyner's hexagonal network only for the model with sectorization. In the model without sectorization, a penalty in sum-MG is incurred whenever one insists on a positive delay-sensitive MG.

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arXiv2020

Distributed Hypothesis Testing with Variable-Length Coding

The problem of distributed testing against independence with variable-length coding is considered when the \emph{average} and not the \emph{maximum} communication load is constrained as in previous works. The paper characterizes the optimum type-II error exponent of a single sensor single decision center system given a maximum type-I error probability when communication is either over a noise-free rate-$R$ link or over a noisy discrete memoryless channel (DMC) with stop-feedback. Specifically, let $ε$ denote the maximum allowed type-I error probability. Then the optimum exponent of the system with a rate-$R$ link under a constraint on the average communication load coincides with the optimum exponent of such a system with a rate $R/(1-ε)$ link under a maximum communication load constraint. A strong converse thus does not hold under an average communication load constraint. A similar observation holds also for testing against independence over DMCs. With variable-length coding and stop-feedback and under an average communication load constraint, the optimum type-II error exponent over a DMC of capacity $C$ equals the optimum exponent under fixed-length coding and a maximum communication load constraint when communication is over a DMC of capacity $C(1-ε)^{-1}$. In particular, under variable-length coding over a DMC with stop feedback a strong converse result does not hold and the optimum error exponent depends on the transition law of the DMC only through its capacity.

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arXiv2020

On Hypothesis Testing Against Independence with Multiple Decision Centers

A distributed binary hypothesis testing problem is studied with one observer and two decision centers. Achievable type-II error exponents are derived for testing against conditional independence when the observer communicates with the two decision centers over one common and two individual noise-free bit pipes and when it communicates with them over a noisy broadcast channel (BC). The results are based on a coding and testing scheme that splits the observations into subblocks, so that transmitter and receivers can independently apply to each subblock either Gray-Wyner coordination coding with side-information or hybrid joint source-channel coding with side-information, followed by a Neyman-Pearson test over the subblocks at the receivers. This approach allows to avoid introducing further error exponents that one would expect from the receivers' decoding operations related to binning or the noisy transmission channel. The derived exponents are shown to be optimal in some special cases when communication is over noise-free links. The results reveal a tradeoff between the type-II error exponents at the two decision centers.

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arXiv2020

Hypothesis Testing Over the Two-hop Relay Network

Coding and testing schemes and the corresponding achievable type-II error exponents are presented for binary hypothesis testing over two-hop relay networks. The schemes are based on cascade source coding techniques and {unanimous decision-forwarding}, the latter meaning that a terminal decides on the null hypothesis only if all previous terminals have decided on the null hypothesis. If the observations at the transmitter, the relay, and the receiver form a Markov chain in this order, then, without loss in performance, the proposed cascade source code can be replaced by two independent point-to-point source codes, one for each hop. The decoupled scheme (combined with decision-forwarding) is shown to attain the optimal type-II error exponents for various instances of "testing against conditional independence." The same decoupling is shown to be optimal also for some instances of "testing against independence," when the observations at the transmitter, the receiver, and the relay form a Markov chain in this order, and when the relay-to-receiver link is of sufficiently high rate. For completeness, the paper also presents an analysis of the Shimokawa-Han-Amari binning scheme for the point-to-point hypothesis testing setup.

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arXiv2020

Improved Converses and Gap Results for Coded Caching

Improved lower bounds on the average and the worst-case rate-memory tradeoffs for the Maddah-Ali&Niesen coded caching scenario are presented. For any number of users and files and for arbitrary cache sizes, the multiplicative gap between the exact rate-memory tradeoff and the new lower bound is less than 2.315 in the worst-case scenario and less than 2.507 in the average-case scenario.

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arXiv2019

Distributed Hypothesis Testing with Variable-Length Coding

This paper characterizes the optimal type-II error exponent for a distributed hypothesis testing-against-independence problem when the \emph{expected} rate of the sensor-detector link is constrained. Unlike for the well-known Ahlswede-Csiszar result that holds under a \emph{maximum} rate constraint and where a strong converse holds, here the optimal exponent depends on the allowed type-I error exponent. Specifically, if the type-I error probability is limited by $ε$, then the optimal type-II error exponent under an \emph{expected} rate constraint $R$ coincides with the optimal type-II error exponent under a \emph{maximum} rate constraint of $(1-ε)R$.

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arXiv2019

Age of Information Aware Cache Updating with File- and Age-Dependent Update Durations

We consider a system consisting of a library of time-varying files, a server that at all times observes the current version of all files, and a cache that at the beginning stores the current versions of all files but afterwards has to update %fresh versions of these files from the server. Unlike previous works, the update duration is not constant but depends on the file and its Age of Information (AoI), i.e., of the time elapsed since it was last updated. The goal of this work is to design an update policy that minimizes the average AoI of all files with respect to a given popularity distribution. Actually a relaxed problem, close to the original optimization problem, is solved and a practical update policy is derived. The update policy relies on the file popularity and on the functions that characterize the update durations of the files depending on their AoI. Numerical simulations show a significant improvement of this new update policy compared to the so-called square-root policy that is optimal under file-independent and constant update durations.

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arXiv2018

Distributed Hypothesis Testing based on Unequal-Error Protection Codes

Coding and testing schemes for binary hypothesis testing over noisy networks are proposed and their corresponding type-II error exponents are derived. When communication is over a discrete memoryless channel (DMC), our scheme combines Shimokawa-Han-Amari's hypothesis testing scheme with Borade's unequal error protection (UEP) for channel coding. A separate source channel coding architecture is employed. The resulting exponent is optimal for the newly introduced class of \emph{generalized testing against conditional independence}. When communication is over a MAC or a BC, our scheme combines hybrid coding with UEP. The resulting error exponent over the MAC is optimal in the case of generalized testing against conditional independence with independent observations at the two sensors, when the MAC decomposes into two individual DMCs. In this case, separate source-channel coding is sufficient; this same conclusion holds also under arbitrarily correlated sensor observations when testing is against independence. For the BC, the error exponents region of hybrid coding with UEP exhibits a tradeoff between the exponents attained at the two decision centers. When both receivers aim at maximizing the error exponents under different hypotheses and the marginal distributions of the sensors' observations are different under these hypotheses, then this tradeoff can be mitigated with the following strategy. The sensor makes a tentative guess on the hypothesis, submits this guess, and applies our coding and testing scheme for the DMC only for the decision center that is not interested in maximizing the exponent under the guessed hypothesis.

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arXiv2017

Benefits of Cache Assignment on Degraded Broadcast Channels

Degraded K-user broadcast channels (BC) are studied when receivers are facilitated with cache memories. Lower and upper bounds are derived on the capacity-memory tradeoff, i.e., on the largest rate of reliable communication over the BC as a function of the receivers' cache sizes, and the bounds are shown to match for some special cases. The lower bounds are achieved by two new coding schemes that benefit from non-uniform cache assignment. Lower and upper bounds are also established on the global capacity-memory tradeoff, i.e., on the largest capacity-memory tradeoff that can be attained by optimizing the receivers' cache sizes subject to a total cache memory budget. The bounds coincide when the total cache memory budget is sufficiently small or sufficiently large, characterized in terms of the BC statistics. For small cache memories, it is optimal to assign all the cache memory to the weakest receiver. In this regime, the global capacity-memory tradeoff grows as the total cache memory budget divided by the number of files in the system. In other words, a perfect global caching gain is achievable in this regime and the performance corresponds to a system where all cache contents in the network are available to all receivers. For large cache memories, it is optimal to assign a positive cache memory to every receiver such that the weaker receivers are assigned larger cache memories compared to the stronger receivers. In this regime, the growth rate of the global capacity-memory tradeoff is further divided by the number of users, which corresponds to a local caching gain. Numerical indicate suggest that a uniform cache-assignment of the total cache memory is suboptimal in all regimes unless the BC is completely symmetric. For erasure BCs, this claim is proved analytically in the regime of small cache-sizes.

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arXiv2015

Joint Cache-Channel Coding over Erasure Broadcast Channels

We consider a cache-aided communications system in which a transmitter communicates with many receivers over an erasure broadcast channel. The system serves as a basic model for communicating on-demand content during periods of high network congestion, where some content can be pre-placed in local caches near the receivers. We formulate the cache-aided communications problem as a joint cache-channel coding problem, and characterise some information-theoretic tradeoffs between reliable communications rates and cache sizes. We show that if the receivers experience different channel qualities, then using unequal cache sizes and joint cache-channel coding improves system efficiency.

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arXiv2013

Coding Schemes and Asymptotic Capacity of the Gaussian Broadcast and Interference Channels with Feedback

A coding scheme is proposed for the memoryless Gaussian broadcast channel with correlated noises and feedback. For all noise correlations other than -1, the gap between the sum-rate the scheme achieves and the full-cooperation bound vanishes as the signal-to-noise ratio tends to infinity. When the correlation coefficient is -1, the gains afforded by feedback are unbounded and the prelog is doubled. When the correlation coefficient is +1 we demonstrate a dichotomy: If the noise variances are equal, then feedback is useless, and otherwise, feedback affords unbounded rate gains and doubles the prelog. The unbounded feedback gains, however, require perfect (noiseless) feedback. When the feedback links are noisy the feedback gains are bounded, unless the feedback noise decays to zero sufficiently fast with the signal-to-noise ratio. Extensions to more receivers are also discussed as is the memoryless Gaussian interference channel with feedback.

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arXiv2013

Cognitive Wyner Networks with Clustered Decoding

We study an interference network where equally-numbered transmitters and receivers lie on two parallel lines, each transmitter opposite its intended receiver. We consider two short-range interference models: the "asymmetric network," where the signal sent by each transmitter is interfered only by the signal sent by its left neighbor (if present), and a "symmetric network," where it is interfered by both its left and its right neighbors. Each transmitter is cognizant of its own message, the messages of the $t_\ell$ transmitters to its left, and the messages of the $t_r$ transmitters to its right. Each receiver decodes its message based on the signals received at its own antenna, at the $r_\ell$ receive antennas to its left, and the $r_r$ receive antennas to its right. For such networks we provide upper and lower bounds on the multiplexing gain, i.e., on the high-SNR asymptotic logarithmic growth of the sum-rate capacity. In some cases our bounds meet, e.g., for the asymmetric network. Our results exhibit an equivalence between the transmitter side-information parameters $t_\ell, t_r$ and the receiver side-information parameters $r_\ell, r_r$ in the sense that increasing/decreasing $t_\ell$ or $t_r$ by a positive integer $δ$ has the same effect on the multiplexing gain as increasing/decreasing $r_\ell$ or $r_r$ by $δ$. Moreover---even in asymmetric networks---there is an equivalence between the left side-information parameters $t_\ell, r_\ell$ and the right side-information parameters $t_r, r_r$.

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arXiv2012

On the Capacity of the Discrete Memoryless Broadcast Channel with Feedback

A coding scheme for the discrete memoryless broadcast channel with {noiseless, noisy, generalized} feedback is proposed, and the associated achievable region derived. The scheme is based on a block-Markov strategy combining the Marton scheme and a lossy version of the Gray-Wyner scheme with side-information. In each block the transmitter sends fresh data and update information that allows the receivers to improve the channel outputs observed in the previous block. For a generalization of Dueck's broadcast channel our scheme achieves the noiseless-feedback capacity, which is strictly larger than the no-feedback capacity. For a generalization of Blackwell's channel and when the feedback is noiseless our new scheme achieves rate points that are outside the no-feedback capacity region. It follows by a simple continuity argument that for both these channels and when the feedback noise is sufficiently low, our scheme improves on the no-feedback capacity even when the feedback is noisy.

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