arXiv subjects

Michèle Wigger

Publications and source records attributed to Michèle Wigger.

At least 55 records · Page 3Linked to original sources

arXiv2020

Some Results on the Vector Gaussian Hypothesis Testing Problem

This paper studies the problem of discriminating two multivariate Gaussian distributions in a distributed manner. Specifically, it characterizes in a special case the optimal typeII error exponent as a function of the available communication rate. As a side-result, the paper also presents the optimal type-II error exponent of a slight generalization of the hypothesis testing against conditional independence problem where the marginal distributions under the two hypotheses can be different.

cs.IT↗

arXiv2020

A Fundamental Storage-Communication Tradeoff for Distributed Computing with Straggling Nodes

Placement delivery arrays for distributed computing (Comp-PDAs) have recently been proposed as a framework to construct universal computing schemes for MapReduce-like systems. In this work, we extend this concept to systems with straggling nodes, i.e., to systems where a subset of the nodes cannot accomplish the assigned map computations in due time. Unlike most previous works that focused on computing linear functions, our results are universal and apply for arbitrary map and reduce functions. Our contributions are as follows. Firstly, we show how to construct a universal coded computing scheme for MapReduce-like systems with straggling nodes from any given Comp-PDA. We also characterize the storage and communication loads of the resulting scheme in terms of the Comp-PDA parameters. Then, we prove an information-theoretic converse bound on the storage-communication (SC) tradeoff achieved by universal computing schemes with straggling nodes. We show that the information-theoretic bound matches the performance achieved by the coded computing schemes with straggling nodes corresponding to the Maddah-Ali and Niesen (MAN) PDAs, i.e., to the Comp-PDAs describing Maddah-Ali and Niesen's coded caching scheme. Interestingly, the same Comp-PDAs (the MAN-PDAs) are optimal for any number of straggling nodes, which implies that the map phase of optimal coded computing schemes does not need to be adapted to the number of stragglers in the system. We finally prove that while the points that lie exactly on the fundamental SC tradeoff cannot be achieved with Comp-PDAs that require smaller number of files than the MAN-PDAs, this is possible for some of the points that lie close to the SC tradeoff. For these latter points, the decrease in the requested number of files can be exponential in the number of nodes of the system.

cs.IT↗

arXiv2020

On the Capacity of MIMO Optical Wireless Channels

This paper studies the capacity of a general multiple-input multiple-output (MIMO) free-space optical intensity channel under a per-input-antenna peak-power constraint and a total average-power constraint over all input antennas. The focus is on the scenario with more transmit than receive antennas. In this scenario, different input vectors can yield identical distributions at the output, when they result in the same image vector under multiplication by the channel matrix. We first determine the most energy-efficient input vectors that attain each of these image vectors. Based on this, we derive an equivalent capacity expression in terms of the image vector, and establish new lower and upper bounds on the capacity of this channel. The bounds match when the signal-to-noise ratio (SNR) tends to infinity, establishing the high-SNR asymptotic capacity. We also characterize the low-SNR slope of the capacity of this channel.

cs.IT↗

arXiv2020

Placement Delivery Array Design for Combination Networks with Edge Caching

A major practical limitation of the Maddah-Ali-Niesen coded caching techniques is their high subpacketization level. For the simple network with a single server and multiple users, Yan \emph{et al.} proposed an alternative scheme with the so-called placement delivery arrays (PDA). Such a scheme requires slightly higher transmission rates but significantly reduces the subpacketization level. In this paper, we extend the PDA framework and propose three low-subpacketization schemes for combination networks, i.e., networks with a single server, multiple relays, and multiple cache-aided users that are connected to subsets of relays. One of the schemes achieves the cutset lower bound on the link rate when the cache memories are sufficiently large. Our other two schemes apply only to \emph{resolvable} combination networks. For these networks and for a wide range of cache sizes, the new schemes perform closely to the coded caching schemes that directly apply Maddah-Ali-Niesen scheme while having significantly reduced subpacketization levels.

cs.IT↗

arXiv2020

A Storage-Computation-Communication Tradeoff for Distributed Computing

This paper investigates distributed computing systems where computations are split into "Map" and "Reduce" functions. A new coded scheme, called distributed computing and coded communication (D3C), is proposed, and its communication load is analyzed as a function of the available storage space and the number of intermediate values (IVA) to be computed. D3C achieves the smallest possible communication load for a given storage space, while a smaller number of IVAs need to be computed compared to Li et al.'s coded distributed computing (CDC) scheme. More generally, our scheme can flexibly trade between storage space and the number of IVAs to be computed. Communication load is then analyzed for any given tradeoff.

cs.IT↗

arXiv2020

Storage, Computation, and Communication: A Fundamental Tradeoff in Distributed Computing

We consider a MapReduce-like distributed computing system. We derive a lower bound on the communication cost for any given storage and computation costs. This lower bound matches the achievable bound we proposed recently. As a result, we completely characterize the optimal tradeoff between the storage, the computation, and the communication. Our result generalizes the previous one by Li et al. to also account for the number of computed intermediate values.

cs.IT↗

arXiv2019

Distributed Hypothesis Testing: Cooperation and Concurrent Detection

A single-sensor two-detectors system is considered where the sensor communicates with both detectors and Detector 1 communicates with Detector 2, all over noise-free rate-limited links. The sensor and both detectors observe discrete memoryless source sequences whose joint probability mass function depends on a binary hypothesis. The goal at each detector is to guess the binary hypothesis in a way that, for increasing observation lengths, the probability of error under one of the hypotheses decays to zero with largest possible exponential decay, whereas the probability of error under the other hypothesis can decay to zero arbitrarily slow. For the setting with zero-rate communication on both links, we exactly characterize the set of possible exponents and the gain brought up by cooperation, in function of the number of bits that are sent over the two links. Notice that, for this setting, tradeoffs between the exponents achieved at the two detectors arise only in few particular cases. In all other cases, each detector achieves the same performance as if it were the only detector in the system. For the setting with positive communication rates from the sensor to the detectors, we characterize the set of all possible exponents in a special case of testing against independence. In this case the cooperation link allows Detector~2 to increase its Type-II error exponent by an amount that is equal to the exponent attained at Detector 1. We also provide a general inner bound on the set of achievable error exponents. For most cases it shows a tradeoff between the two exponents.

cs.IT↗

arXiv2019

Multiplexing Gain Region of Sectorized Cellular Networks with Mixed Delay Constraints

The sectorized hexagonal model with mixed delay constraints is considered when both neighbouring mobile users and base stations can cooperate over rate-limited links. Each message is a combination of independent "fast" and "slow" bits, where the former are subject to a stringent delay constraint and cannot profit from cooperation. Inner and outer bounds on the multiplexing gain region are derived. The obtained results show that for small cooperation prelogs or moderate "fast" multiplexing gains, the overall performance (sum multiplexing gain) is hardly decreased by the stringent delay constraints on the "fast" bits. For large cooperation prelogs and large "fast" multiplexing gains, increasing the "fast" multiplexing gain by $Δ$ comes at the expense of decreasing the sum multiplexing gain by $3 Δ$.

cs.IT↗

arXiv2018

Distributed Hypothesis Testing with Collaborative Detection

A detection system with a single sensor and two detectors is considered, where each of the terminals observes a memoryless source sequence, the sensor sends a message to both detectors and the first detector sends a message to the second detector. Communication of these messages is assumed to be error-free but rate-limited. The joint probability mass function (pmf) of the source sequences observed at the three terminals depends on an $\mathsf{M}$-ary hypothesis $(\mathsf{M} \geq 2)$, and the goal of the communication is that each detector can guess the underlying hypothesis. Detector $k$, $k=1,2$, aims to maximize the error exponent \textit{under hypothesis} $i_k$, $i_k \in \{1,\ldots,\mathsf{M}\}$, while ensuring a small probability of error under all other hypotheses. We study this problem in the case in which the detectors aim to maximize their error exponents under the \textit{same} hypothesis (i.e., $i_1=i_2$) and in the case in which they aim to maximize their error exponents under \textit{distinct} hypotheses (i.e., $i_1 \neq i_2$). For the setting in which $i_1=i_2$, we present an achievable exponents region for the case of positive communication rates, and show that it is optimal for a specific case of testing against independence. We also characterize the optimal exponents region in the case of zero communication rates. For the setting in which $i_1 \neq i_2$, we characterize the optimal exponents region in the case of zero communication rates.

cs.IT↗

arXiv2018

Distributed Hypothesis Testing with Concurrent Detections

A detection system with a single sensor and $\mathsf{K}$ detectors is considered, where each of the terminals observes a memoryless source sequence and the sensor sends a common message to all the detectors. The communication of this message is assumed error-free but rate-limited. The joint probability mass function (pmf) of the source sequences observed at the terminals depends on an $\mathsf{M}$-ary hypothesis $(\mathsf{M} \geq \mathsf{K})$, and the goal of the communication is that each detector can guess the underlying hypothesis. Each detector $k$ aims to maximize the error exponent under hypothesis $k$, while ensuring a small probability of error under all other hypotheses. This paper presents an achievable exponents region for the case of positive communication rate, and characterizes the optimal exponents region for the case of zero communication rate. All results extend also to a composite hypothesis testing scenario.

cs.IT↗

arXiv2018

State-Adaptive Coded Caching for Symmetric Broadcast Channels

Coded-caching delivery is considered over a symmetric noisy broadcast channel whose state is unknown at the transmitter during the cache placement phase. In particular, the delivery phase is modeled by a state-dependent broadcast channel where the state remains constant over each transmission block and is learned by the transmitter (and the receivers) only at the beginning of each block. A state-adaptive coded caching scheme is proposed that improves either on rate or decoding latency over two baseline schemes that are based on standard coded caching.

cs.IT↗

arXiv2018

Mixed Delay Constraints in Wyner's Soft-Handoff Network

Wyner's soft-handoff network with mixed delay constraints is considered when neighbouring receivers can cooperate over rate-limited links. Each source message is a combination of independent "fast" and "slow" bits, where the former are subject to a stringent decoding delay. Inner and outer bounds on the capacity region are derived, and the multiplexing gain region is characterized when only transmitters or only receivers cooperate.

cs.IT↗

arXiv2018

Secrecy Capacity-Memory Tradeoff of Erasure Broadcast Channels

This paper derives upper and lower bounds on the secrecy capacity-memory tradeoff of a wiretap erasure broadcast channel (BC) with Kw weak receivers and Ks strong receivers, where weak receivers, respectively strong receivers, have same erasure probabilities and cache sizes. The lower bounds are achieved by schemes that meticulously combine joint cache-channel coding with wiretap coding and key-aided one-time pads. The presented upper bound holds more generally for arbitrary degraded BCs and arbitrary cache sizes. When only weak receivers have cache memories, upper and lower bounds coincide for small and large cache memories, thus providing the exact secrecy capacity-memory tradeoff for this setup. The derived bounds allow to further conclude that the secrecy capacity is positive even when the eavesdropper is stronger than all the legitimate receivers with cache memories. Moreover, they show that the secrecy capacity-memory tradeoff can be significantly smaller than its non-secure counterpart, but it grows much faster when cache memories are small. The paper also presents a lower bound on the global secrecy capacity-memory tradeoff where one is allowed to optimize the cache assignment subject to a total cache budget. It is close to the best known lower bound without secrecy constraint. For small total cache budget, the global secrecy capacity-memory tradeoff is achieved by assigning all the available cache memory uniformly over all receivers if the eavesdropper is stronger than all legitimate receivers, and it is achieved by assigning the cache memory uniformly only over the weak receivers if the eavesdropper is weaker than the strong receivers.

cs.IT↗

arXiv2017

Capacity Results on Multiple-Input Single-Output Wireless Optical Channels

This paper derives upper and lower bounds on the capacity of the multiple-input single-output free-space optical intensity channel with signal-independent additive Gaussian noise subject to both an average-intensity and a peak-intensity constraint. In the limit where the signal-to-noise ratio (SNR) tends to infinity, the asymptotic capacity is specified, while in the limit where the SNR tends to zero, the exact slope of the capacity is also given.

cs.IT↗

arXiv2017

Feedback and Partial Message Side-Information on the Semideterministic Broadcast Channel

The capacity of the semideterministic discrete memoryless broadcast channel (SD-BC) with partial message side-information (P-MSI) at the receivers is established. In the setting without a common message, it is shown that P-MSI to the stochastic receiver alone can increase capacity, whereas P-MSI to the deterministic receiver can only increase capacity if also the stochastic receiver has P-MSI. The latter holds only for the setting without a common message: if the encoder also conveys a common message, then P-MSI to the deterministic receiver alone can increase capacity. These capacity results are used to show that feedback from the stochastic receiver can increase the capacity of the SD-BC without P-MSI and the sum-rate capacity of the SD-BC with P-MSI at the deterministic receiver. The link between P-MSI and feedback is a feedback code, which---roughly speaking---turns feedback into P-MSI at the stochastic receiver and hence helps the stochastic receiver mitigate experienced interference. For the case where the stochastic receiver has full MSI (F-MSI) and can thus fully mitigate experienced interference also in the absence of feedback, it is shown that feedback cannot increase capacity.

cs.IT↗

arXiv2016

On Achievability for Downlink Cloud Radio Access Networks with Base Station Cooperation

This work investigates the downlink of a cloud radio access network (C-RAN) in which a central processor communicates with two mobile users through two base stations (BSs). The BSs act as relay nodes and cooperate with each other through error-free rate-limited links. We develop and analyze two coding schemes for this scenario. The first coding scheme is based on Liu-Kang scheme for C-RANs without BS cooperation; and extends it to scenarios allowing conferencing between the BSs. Among few other features, our new coding scheme enables arbitrary correlation among the auxiliary codewords that are recovered by the BSs. It also introduces common codewords to be described to both BSs. For the analysis of this coding scheme, we extend the multivariate covering lemma to non-Cartesian product sets, thereby correcting an erroneous application of this lemma in Liu-Kang's related work. We highlight key aspects of this scheme by studying three important instances of it. The second coding scheme extends the so-called compression scheme that was originally developed for memoryless Gaussian C-RANs without BS cooperation to general discrete memoryless C-RANs with BS cooperation. We show that this scheme subsumes the original compression scheme when applied to memoryless Gaussian C-RAN models. In the analysis of this scheme, we also highlight important connections with the so-called distributed decode--forward scheme, and refine the approximate capacity of a general $N$-BS $L$-user C-RAN model in the memoryless Gaussian case.

cs.IT↗

arXiv2016

A Rate-Distortion Approach to Caching

This paper takes a rate-distortion approach to understanding the information-theoretic laws governing cache-aided communications systems. Specifically, we characterise the optimal tradeoffs between the delivery rate, cache capacity and reconstruction distortions for a single-user problem and some special cases of a two-user problem. Our analysis considers discrete memoryless sources, expected- and excess-distortion constraints, and separable and f-separable distortion functions. We also establish a strong converse for separable-distortion functions, and we show that lossy versions of common information (Gács-Körner and Wyner) play an important role in caching. Finally, we illustrate and explicitly evaluate these laws for multivariate Gaussian sources and binary symmetric sources.

cs.IT↗

arXiv2016

Complete Interference Mitigation Through Receiver-Caching in Wyner's Networks

We present upper and lower bounds on the per-user multiplexing gain (MG) of Wyner's circular soft-handoff model and Wyner's circular full model with cognitive transmitters and receivers with cache memories. The bounds are tight for cache memories with prelog $μ\geq 2/3D$ in the soft-handoff model and for $μ\geq D$ in the full model, where $D$ denotes the number of possibly demanded files. In these cases the per-user MG of the two models is $1+μ/D$, the same as for non-interfering point-to-point links with caches at the receivers. Large receiver cache-memories thus allow to completely mitigate interference in these networks.

cs.IT↗