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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: closed (30 September 2020) | Viewed by 22310

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Prof. Dr. H. Vincent Poor

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Guest Editor

Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ 08544, USA
Interests: information theory; statistical signal processing; stochastic analysis
Special Issues, Collections and Topics in MDPI journals

Dr. Alex Dytso

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Guest Editor

Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA
Interests: multi-user information theory and estimation theory and their applications in wireless networks
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Network information theory is a framework for studying performance limits in communications over networks; as such, it is expected to continue to play an essential role in the future development of wireless networks, including 5G and beyond. This Special Issue aims to bring together the body of recent results in network information theory, in order to bolster its value and emphasize the importance it continues to play in the development of wireless communications. Previously unpublished contributions in the intersection networks information theory and wireless networks are solicited, including (but not limited to) the following:

Emerging information theoretic models for wireless communications;
Gaussian networks;
Capacity scaling laws;
Massive networks;
Random access;
Interference mitigation schemes;
Relaying techniques;
MIMO channels;
Massive MIMO;
Low latency communications;
Secure and private communications;
Low power communications;
Code design for networks;
Interactive communications and feedback;
Communication under channel uncertainty;
Mismatched network capacity;
Cloud and fog radio access networks.

All submitted manuscripts will be peer-reviewed, and accepted papers will be available via open access.

Prof. Dr. H. Vincent Poor
Dr. Alex Dytso
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Related Special Issue

Wireless Networks: Information Theoretic Perspectives III in Entropy (3 articles)

Published Papers (9 papers)

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Research

26 pages, 444 KiB

Open AccessArticle

MISO Broadcast Channel under Unequal Link Coherence Times and Channel State Information

by Mohamed Fadel Shady and Aria Nosratinia

Entropy 2020, 22(9), 976; https://doi.org/10.3390/e22090976 - 01 Sep 2020

Cited by 3 | Viewed by 2077

Abstract

The broadcast channel may experience unequal link coherence times due to a number of factors including variation in node mobility or local scattering conditions. This means the block fading model for different links may have nonidentical block length, and the channel state information for the links may also not be identical. The faster the fading and the shorter the fading block length, the more often the link needs to be trained and estimated at the receiver, and the more likely that channel state information (CSI) is stale or unavailable at the transmitter. This paper investigates a MISO broadcast channel where some receivers experience longer coherence intervals and other receivers experience shorter coherence intervals and must estimate their receive-side CSI (CSIR) frequently. We consider a variety of transmit-side CSI (CSIT) conditions for the abovementioned model, including no CSIT, delayed CSIT, or hybrid CSIT. To investigate the degrees of freedom region, we employ interference alignment and beamforming along with a product superposition that allows simultaneous but noncontaminating transmission of pilots and data to different receivers. Outer bounds employ the extremal entropy inequality as well as a bounding of the performance of a discrete, memoryless, multiuser, multilevel broadcast channel. For several cases, inner and outer bounds are established that either partially meet, or the gap diminishes with increasing coherence times. Full article

(This article belongs to the Special Issue Wireless Networks: Information Theoretic Perspectives)

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39 pages, 1404 KiB

Open AccessArticle

An Upper Bound on the Error Induced by Saddlepoint Approximations—Applications to Information Theory

by Dadja Anade, Jean-Marie Gorce, Philippe Mary and Samir M. Perlaza

Entropy 2020, 22(6), 690; https://doi.org/10.3390/e22060690 - 20 Jun 2020

Cited by 6 | Viewed by 2515

Abstract

This paper introduces an upper bound on the absolute difference between:

(a)

the cumulative distribution function (CDF) of the sum of a finite number of independent and identically distributed random variables with finite absolute third moment; and

(b)

a [...] Read more.

This paper introduces an upper bound on the absolute difference between:

(a)

the cumulative distribution function (CDF) of the sum of a finite number of independent and identically distributed random variables with finite absolute third moment; and

(b)

a saddlepoint approximation of such CDF. This upper bound, which is particularly precise in the regime of large deviations, is used to study the dependence testing (DT) bound and the meta converse (MC) bound on the decoding error probability (DEP) in point-to-point memoryless channels. Often, these bounds cannot be analytically calculated and thus lower and upper bounds become particularly useful. Within this context, the main results include, respectively, new upper and lower bounds on the DT and MC bounds. A numerical experimentation of these bounds is presented in the case of the binary symmetric channel, the additive white Gaussian noise channel, and the additive symmetric

α

-stable noise channel. Full article

(This article belongs to the Special Issue Wireless Networks: Information Theoretic Perspectives)

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14 pages, 401 KiB

Open AccessArticle

Stealthy Secret Key Generation

by Pin-Hsun Lin, Carsten R. Janda, Eduard A. Jorswieck and Rafael F. Schaefer

Entropy 2020, 22(6), 679; https://doi.org/10.3390/e22060679 - 18 Jun 2020

Cited by 4 | Viewed by 2203

Abstract

In order to make a warden, Willie, unaware of the existence of meaningful communications, there have been different schemes proposed including covert and stealth communications. When legitimate users have no channel advantage over Willie, the legitimate users may need additional secret keys to confuse Willie, if the stealth or covert communication is still possible. However, secret key generation (SKG) may raise Willie’s attention since it has a public discussion, which is observable by Willie. To prevent Willie’s attention, we consider the source model for SKG under a strong secrecy constraint, which has further to fulfill a stealth constraint. Our first contribution is that, if the stochastic dependence between the observations at Alice and Bob fulfills the strict more capable criterion with respect to the stochastic dependence between the observations at Alice and Willie or between Bob and Willie, then a positive stealthy secret key rate is identical to the one without the stealth constraint. Our second contribution is that, if the random variables observed at Alice, Bob, and Willie induced by the common random source form a Markov chain, then the key capacity of the source model SKG with the strong secrecy constraint and the stealth constraint is equal to the key capacity with the strong secrecy constraint, but without the stealth constraint. For the case of fast fading models, a sufficient condition for the existence of an equivalent model, which is degraded, is provided, based on stochastic orders. Furthermore, we present an example to illustrate our results. Full article

(This article belongs to the Special Issue Wireless Networks: Information Theoretic Perspectives)

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32 pages, 1990 KiB

Open AccessArticle

Degrees-Of-Freedom in Multi-Cloud Based Sectored Cellular Networks

by Samet Gelincik and Ghaya Rekaya-Ben Othman

Entropy 2020, 22(6), 668; https://doi.org/10.3390/e22060668 - 16 Jun 2020

Cited by 3 | Viewed by 2023

Abstract

This paper investigates the achievable per-user degrees-of-freedom (DoF) in multi-cloud based sectored hexagonal cellular networks (M-CRAN) at uplink. The network consists of N base stations (BS) and

K \leq N

base band unit pools (BBUP), which function as independent cloud centers. The [...] Read more.

K \leq N

base band unit pools (BBUP), which function as independent cloud centers. The communication between BSs and BBUPs occurs by means of finite-capacity fronthaul links of capacities

C_{F} = μ_{F} \cdot \frac{1}{2} \log (1 + P)

with P denoting transmit power. In the system model, BBUPs have limited processing capacity

C_{BBU} = μ_{BBU} \cdot \frac{1}{2} \log (1 + P)

. We propose two different achievability schemes based on dividing the network into non-interfering parallelogram and hexagonal clusters, respectively. The minimum number of users in a cluster is determined by the ratio of BBUPs to BSs,

r = K / N

. Both of the parallelogram and hexagonal schemes are based on practically implementable beamforming and adapt the way of forming clusters to the sectorization of the cells. Proposed coding schemes improve the sum-rate over naive approaches that ignore cell sectorization, both at finite signal-to-noise ratio (SNR) and in the high-SNR limit. We derive a lower bound on per-user DoF which is a function of

μ_{BBU}

μ_{F}

, and r. We show that cut-set bound are attained for several cases, the achievability gap between lower and cut-set bounds decreases with the inverse of BBUP-BS ratio

\frac{1}{r}

for

μ_{F} \leq 2 M

irrespective of

μ_{BBU}

, and that per-user DoF achieved through hexagonal clustering can not exceed the per-user DoF of parallelogram clustering for any value of

μ_{BBU}

and r as long as

μ_{F} \leq 2 M

. Since the achievability gap decreases with inverse of the BBUP-BS ratio for small and moderate fronthaul capacities, the cut-set bound is almost achieved even for small cluster sizes for this range of fronthaul capacities. For higher fronthaul capacities, the achievability gap is not always tight but decreases with processing capacity. However, the cut-set bound, e.g., at

\frac{5 M}{6}

, can be achieved with a moderate clustering size. Full article

(This article belongs to the Special Issue Wireless Networks: Information Theoretic Perspectives)

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31 pages, 895 KiB

Open AccessArticle

On the Downlink Capacity of Cell-Free Massive MIMO with Constrained Fronthaul Capacity

by Peng Zhang and Frans M. J. Willems

Entropy 2020, 22(4), 418; https://doi.org/10.3390/e22040418 - 07 Apr 2020

Cited by 5 | Viewed by 3190

Abstract

We investigate the downlink of a cell-free massive multiple-in multiple-out system in which all access points (APs) are connected in a linear-topolpgy fronthaul with constrained capacity and send a common message to a single receiver. By modeling the system as an extension of the multiple-access channel with partially cooperating encoders, we derive the channel capacity of the two-AP setting and then extend the results to arbitrary N-AP scenarios. By developing a cooperating mode concept, we investigate the optimal cooperation among the encoders (APs) when we limit the total fronthaul capacity, and the total transmit power is constrained as well. It is demonstrated that achieving capacity requires a water-pouring distribution of the total available fronthaul capacity over the fronthaul links. Our study reveals that a linear growth of total fronthaul capacity results in a logarithmic growth of the beamforming capacity. Moreover, even if the number of APs would be unlimited, only a finite number of them need to be activated. We found an expression for this number. Full article

(This article belongs to the Special Issue Wireless Networks: Information Theoretic Perspectives)

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34 pages, 667 KiB

Open AccessArticle

On the Rate-Distortion Function of Sampled Cyclostationary Gaussian Processes

by Emeka Abakasanga, Nir Shlezinger and Ron Dabora

Entropy 2020, 22(3), 345; https://doi.org/10.3390/e22030345 - 17 Mar 2020

Cited by 1 | Viewed by 2228

Abstract

Man-made communications signals are typically modelled as continuous-time (CT) wide-sense cyclostationary (WSCS) processes. As modern processing is digital, it is applied to discrete-time (DT) processes obtained by sampling the CT processes. When sampling is applied to a CT WSCS process, the statistics of the resulting DT process depends on the relationship between the sampling interval and the period of the statistics of the CT process: When these two parameters have a common integer factor, then the DT process is WSCS. This situation is referred to as synchronous sampling. When this is not the case, which is referred to as asynchronous sampling, the resulting DT process is wide-sense almost cyclostationary (WSACS). The sampled CT processes are commonly encoded using a source code to facilitate storage or transmission over wireless networks, e.g., using compress-and-forward relaying. In this work, we study the fundamental tradeoff between rate and distortion for source codes applied to sampled CT WSCS processes, characterized via the rate-distortion function (RDF). We note that while RDF characterization for the case of synchronous sampling directly follows from classic information-theoretic tools utilizing ergodicity and the law of large numbers, when sampling is asynchronous, the resulting process is not information stable. In such cases, the commonly used information-theoretic tools are inapplicable to RDF analysis, which poses a major challenge. Using the information-spectrum framework, we show that the RDF for asynchronous sampling in the low distortion regime can be expressed as the limit superior of a sequence of RDFs in which each element corresponds to the RDF of a synchronously sampled WSCS process (yet their limit is not guaranteed to exist). The resulting characterization allows us to introduce novel insights on the relationship between sampling synchronization and the RDF. For example, we demonstrate that, differently from stationary processes, small differences in the sampling rate and the sampling time offset can notably affect the RDF of sampled CT WSCS processes. Full article

(This article belongs to the Special Issue Wireless Networks: Information Theoretic Perspectives)

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30 pages, 484 KiB

Open AccessArticle

Multiplexing Gains under Mixed-Delay Constraints on Wyner’s Soft-Handoff Model

by Homa Nikbakht, Michèle Angela Wigger and Shlomo Shamai (Shitz)

Entropy 2020, 22(2), 182; https://doi.org/10.3390/e22020182 - 05 Feb 2020

Cited by 6 | Viewed by 1933

Abstract

This paper analyzes the multiplexing gains (MG) achievable over Wyner’s soft-handoff model under mixed-delay constraints, that is, when delay-sensitive and delay-tolerant data are simultaneously transmitted over the network. In the considered model, delay-sensitive data cannot participate or profit in any ways from transmitter or receiver cooperation, but delay-tolerant data can. Cooperation for delay-tolerant data takes place over rate-limited links and is limited to a fixed number of cooperation rounds. For the described setup, inner and outer bounds are derived on the set of MG pairs that are simultaneously achievable for delay-sensitive and delay-tolerant data. The bounds are tight in special cases and allow us to obtain the following conclusions. For large cooperation rates, and when both transmitters and receivers can cooperate, it is possible to simultaneously attain maximum MG for delay-sensitive messages and maximum sum MG for all messages. For comparison, in scheduling schemes (also called time-sharing schemes), the largest achievable sum MG decreases linearly with the MG of delay-sensitive messages. A similar linear decrease is proved for any coding scheme, not only for scheduling schemes, if only transmitters or only receivers can cooperate (but not both) and if delay-sensitive messages have moderate MG. In contrast, if the MG of delay-sensitive messages is small, the maximum sum MG can be achieved even with only transmitter or only receiver cooperation. To summarise, when cooperation rates are high and both transmitters and receivers can cooperate or when delay-sensitive messages have small MG, then transmitting delay-sensitive messages causes no penalty on the sum-MG. In other regimes, this penalty increases proportionally to the delay-tolerant MG in the sense that increasing the delay-sensitive MG by

Δ

penalises the largest achievable delay-tolerant MG by

2 Δ

and thus the sum MG by

Δ

. Full article

(This article belongs to the Special Issue Wireless Networks: Information Theoretic Perspectives)

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26 pages, 1724 KiB

Open AccessArticle

Secure Retrospective Interference Alignment

by Mohamed Seif, Ravi Tandon and Ming Li

Entropy 2019, 21(11), 1092; https://doi.org/10.3390/e21111092 - 07 Nov 2019

Cited by 3 | Viewed by 2317

Abstract

In this paper, the K-user interference channel with secrecy constraints is considered with delayed channel state information at transmitters (CSIT). We propose a novel secure retrospective interference alignment scheme in which the transmitters carefully mix information symbols with artificial noises to ensure confidentiality. Achieving positive secure degrees of freedom (SDoF) is challenging due to the delayed nature of CSIT, and the distributed nature of the transmitters. Our scheme works over two phases: Phase one, in which each transmitter sends information symbols mixed with artificial noises, and repeats such transmission over multiple rounds. In the next phase, each transmitter uses the delayed CSIT of the previous phase and sends a function of the net interference and artificial noises (generated in previous phase), which is simultaneously useful for all receivers. These phases are designed to ensure the decodability of the desired messages while satisfying the secrecy constraints. We present our achievable scheme for three models, namely: (1) K-user interference channel with confidential messages (IC-CM), and we show that

\frac{1}{2} (\sqrt{K} - 6)

SDoF is achievable; (2) K-user interference channel with an external eavesdropper (IC-EE); and (3) K-user IC with confidential messages and an external eavesdropper (IC-CM-EE). We show that for the K-user IC-EE,

\frac{1}{2} (\sqrt{K} - 3)

SDoF is achievable, and for the K-user IC-CM-EE,

\frac{1}{2} (\sqrt{K} - 6)

is achievable. To the best of our knowledge, this is the first result on the K-user interference channel with secrecy constrained models and delayed CSIT that achieves an SDoF which scales with

\sqrt{K}

, square-root of number of users. Full article

(This article belongs to the Special Issue Wireless Networks: Information Theoretic Perspectives)

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12 pages, 345 KiB

Open AccessArticle

Ergodic Rate for Fading Interference Channels with Proper and Improper Gaussian Signaling

by Mohammad Soleymani, Ignacio Santamaria, Christian Lameiro and Peter J. Schreier

Entropy 2019, 21(10), 922; https://doi.org/10.3390/e21100922 - 23 Sep 2019

Cited by 8 | Viewed by 2903

Abstract

This paper studies the performance of improper Gaussian signaling (IGS) over a 2-user Rayleigh single-input single-output (SISO) interference channel, treating interference as noise. We assume that the receivers have perfect channel state information (CSI), while the transmitters have access to only statistical CSI. Under these assumptions, we consider a signaling scheme, which we refer to as proper/improper Gaussian signaling or PGS/IGS, where at most one user may employ IGS. For the Rayleigh fading channel model, we characterize the statistical distribution of the signal-to-interference-plus-noise ratio at each receiver and derive closed-form expressions for the ergodic rates. By adapting the powers, we characterize the Pareto boundary of the ergodic rate region for the 2-user fading IC. The ergodic transmission rates can be attained using fixed-rate codebooks and no optimization is involved. Our results show that, in the moderate and strong interference regimes, the proposed PGS/IGS scheme improves the performance with respect to the PGS scheme. Additionally, we numerically compute the ergodic rate region of the full IGS scheme when both users can employ IGS and their transmission parameters are optimized by an exhaustive search. Our results suggest that most of the Pareto optimal points for the 2-user fading IC channel are attained when either both users transmit PGS or when one transmits PGS and the other transmits maximally improper Gaussian signals and time sharing is allowed. Full article

(This article belongs to the Special Issue Wireless Networks: Information Theoretic Perspectives)

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