Section: New Results
Results of axis 1: fundamental limits
We worked in 2019 on the following main research directions:

Fundamental limits of IoT networks
Table 1. Principal Investigators: Malcolm Egan, Samir Perlaza, JeanMarie Gorce Students: Dadja Toussaint AnadeAkbo, Lélio Chetot Funding: Orange Labs, ANR Arburst Partners: Philippe Mary (IETR, Rennes), Laurent Clavier (IRCICA, Lille) JM Kélif (Orange Labs) H. Vincent Poor (Princeton University, NJ, USA) Publications: [34], [48], [36], [49], [35] One of the main figures of merit in an IoT cell is the capability to support a massive access from distributed nodes, but with very small information quantity [12]. This perspective raises fundamental questions relative to the theoretical limits and performance of this kind of very large scale deployments. Fundamental limits are neither well known nor even well formulated. What is the maximal number of IoT nodes we may deploy in a given environment? At which energetic cost? With which transmission reliability or latency? These multiple questions highlight that the problem is not unique and the capacity is not the only (and even not the main) challenge to be addressed. We aim at establishing the fundamental limits of a decentralized system in a bursty regime which includes short packets of information and impulsive interference regime. We are targeting the fundamental limits and their mathematical expression, according to the usual information theory framework capturing the capacity region by establishing converse and achievability theorems.

Stability and sensitivity of fundamental limits
Table 2. Principal Investigator: Malcolm Egan, Samir Perlaza Students:  Funding: Partners: H. Vincent Poor, Alex Disto, Princeton University Vyacheslav Kungurtsev, Czech Technical University Publications: [8],[33] The analysis of the fundamental limits on communications systems is performed under some assumptions including Gaussian noise, channel input symbols with average power, among others. Nonetheless, despite that these constraints were well suited for describing communications systems in the early 90’s, the evolution of these systems make these assumptions vacuous today. Often, noise is better described by $\alpha $–stable stochastic processes in IoT networks and channel inputs are subject to constraints in the amplitude, energy harvesting etc. From this perspective, our contributions are based on the notion of capacity sensitivity to study the capacity of continuous memoryless pointtopoint channels. The capacity sensitivity reflects how the capacity changes with small perturbations in any of the parameters describing the channel, e.g., cost constraints on the input distribution as well as on the noise distribution.

Energy selfsustained wireless networks
Table 3. Principal Investigator: Samir Perlaza Students: Nizar Khalfet Funding: H2020 ComMed Partners: I. Kikridis (U. of Cyprus) Publications: [29], [42], [43], [50] The main scientific challenge is to set up a theoretical framework for designing and developing fully decentralized energyselfsustained communications systems. The main motivation stems from the fact that wireless networks deployed in hardtoreach places, e.g., remote geographical areas, concrete structures, human body or war zones are often limited by the lifetime of their batteries. This contrasts with the fact that hardware is built to last for very long periods. One of the solutions being considered today for solving the energy limitation problem is the use of energy harvesting (EH) techniques. Within this context, our work focuses on the study of wireless communications systems based on EH sources. EH is expected to be the enabler of energy selfsustainability by eliminating the critical dependence on manual battery recharging.
However, a solid answer on whether or not EH is a viable solution can be given only if the corresponding fundamental limits of data transmission based on EH are known. This is mainly because these limits are based on the laws of Physics and thus, determine the barrier between feasible and unfeasible systems. We study the fundamental limits of three strongly correlated problems regarding the energy supply of future wireless networks: (i) Data transmission over centralized and decentralized EH multiuser channels; (ii) Simultaneous energy and information transmission in multiuser channels; and (iii) Energy cooperation. In a near future, we expect to exploit these results to design algorithms and protocols and later to perform a proof of concept on FIT/CorteXlab. We believe that a solid theoretical framework may help to drive the future design and performance evaluation of applications involving EH based wireless communications systems within smart buildings, smart cities.

Table 4. Principal Investigator: Samir Perlaza Students: David Kibloff Funding: InriaDGA PhD Partners: Guilaume Villemaud (Socrate), Ligong Wang (ETIS, Cergy) Raphael Shaeffer (TU Berlin) Publications: [44], [51] Information theory is also well adapted to study the fundamental limits of privacy and secrecy. Indeed, the wiretap channel and the covert communication [53] models have been shown to be appropriate for privacy preserving communications in wireless communications. With the PhD of David Kibloff defended in October 2019, we explored the following problem. Given a code used to send a message to two receivers through a degraded discrete memoryless broadcast channel (DMBC), the sender wishes to alter the codewords to achieve the following goals: (i) the original broadcast communication continues to take place, possibly at the expense of a tolerable increase of the decoding error probability; and (ii) an additional covert message can be transmitted to the stronger receiver such that the weaker receiver cannot detect the existence of this message. The main results are: (a) feasibility of covert communications is proven by using a random coding argument for general DMBCs; and (b) necessary conditions for establishing covert communications are described and an impossibility (converse) result is presented for a particular class of DMBCs. Together, these results characterize the asymptotic fundamental limits of covert communications for this particular class of DMBCs within an arbitrarily small gap. Future extensions will concern the Gaussian and other continuous channels, or more complex scenarios where some subsets of nodes are willing to communicate while some external observers cannot even detect the existence of these messages. Covert communication allows to introduce a side constraint that prevent a network to be attacked.

Structured Codes for Quantization and Channel Estimation
Table 5. Principal Investigator: Malcolm Egan Publications: [25] Finite frames are sequences of vectors in finite dimensional Hilbert spaces that play a key role in signal processing and coding theory. In this work, we study the class of tight unitnorm frames for ${\u2102}^{d}$ that also form regular schemes, which we call tight regular schemes (TRS). Many common frames that arising in vector quantization and channel state estimation, such as equiangular tight frames and mutually unbiased bases, fall in this class. We investigate characteristic properties of TRSs and prove that for many constructions, they are intimately connected to weighted 1designs—arising from cubature rules for integrals over spheres in ${\u2102}^{d}$—with weights dependent on the Voronoi regions of each frame element. Aided by additional numerical evidence, we conjecture that all TRSs in fact satisfy this property.