What: PhD position on the fully funded ANR ARBurst project (2016-2021)
Where: CITI Lab / INSA Lyon and IETR / INSA Rennes, FRANCE
When: As soon as possible - duration: 36 months
Topic: Non asymptotic information theory and continuous user density model to assess the fundamental performance bounds of Internet of Things networks
Grants: All inclusive funds for international conferences and project meeting in France. Possibility to take Master students.
CITI Lab. Centre of Innovation in Telecommunications and Integration of Service (http://www.citi-lab.fr)
Start date : As soon as possible – duration : 36 months
This PhD position takes part of the fully funded ANR project ARBurst in collaboration with INSA/IETR Rennes and IRCICA Lille.
With the recent development of machine-to-machine (M2M) communications and internet-of-things (IoT) networks, the infrastructures have to support more users (or nodes) but each of them requesting a very small quantity of information. This project aims at defining a more appropriate formalism allowing to estimate the theoretical limits of M2M communications. The performance of large scale networks has been widely studied during the past 10 years with usual theoretical tools such as Shannon theory or stochastic geometry. These tools provided interesting insights about scaling laws and theoretical limits but with a limited applicability in the context of M2M, IoT and future 5G services due to the inherent spurious and bursty nature of the associated information flows. While the small packet size invalidates the use of the asymptotic Shannon capacity as a performance indicator, the consequent bursty nature also invalidates the Gaussian assumption usually used to model the interference distribution. As a consequence fundamental limits are neither well known nor even well formulated. The goal of the PhD is to propose new design criteria for IoT/M2M networks based on the non-asymptotic information theory framework  but taking into account bursty communications, i.e. use of non-Gaussian interference distribution , and large-scale deployment, i.e. use of stochastic geometry tool .
The candidate will first address the problem of the non-asymptotic bounds (achievability and converse) in network asymptotic regime, i.e. with a spatial continuum of nodes. The main challenge here is to derive the channel dispersion when an infinite number of nodes is considered in multiple access channel (MAC) and broadcast channel (BC) scenarios [1,5]. The inherent dependence between the rate and the error-probability in finite blocklength regime will help us to define a multi-objective framework for the evaluation of IoT/M2M network performances.
Then, the candidate will concentrate on the problem of the non-asymptotic bounds in a non-Gaussian peer-to-peer (P2P) link. The impulsive noise could be represented by an alpha-stable distribution or other distribution able to capture the impulsiveness of the noise. The Polyanskiy’s approach will be investigated trough the kappa-beta bound method for the achievability part. One the challenge would be to derive an expression (or compute) the dispersion of the impulsive channel . The MolavianJazi’s method , based on the central limit theorem (CLT) for functions, could also be investigated in order to approach the mutual information density for stable noise.
Based on these results, the PhD candidate will extend the previous approaches to the multi-user case, by merging the results obtained with spatial continuum of users for MAC/BC scenarios and the channel dispersion for impulsive noise. Based on the outage-splitting theorem for Gaussian MAC , the candidate will address the problem of the achievable region of MAC/BC in impulsive noise. In Gaussian framework, the achievable region of multi-user communications is derived under finite second-order moment. This assumption does not hold in impulsive noise, overall if alpha-stable distributions are considered, alternative constraint-cost functions need to be considered. A part of the research will consist to clearly define on which assumptions the achievability can be studied in bursty context.
The work proposed in this PhD could be of a great importance for industrial actors and researchers in the deployment of the future IoT networks. The limits derived in the thesis could provide guidelines to sustain the dramatic increase of the number of connected devices by giving a set of design criteria for these networks.
 Y. Polyanskiy, H. V. Poor and S. Verdu, “Channel coding rate in the finite blocklength regime”, IEEE Transactions on Information Theory, vol. 56, no. 5, pp. 2307-2359, May 2010.
 G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapmann and Hall, 1994.
 F. Baccelli and B. Blaszczyszyn, “Stochastic geometry and wireless networks: volume 1 theory”, Foundations and Trends in Networking, Vol. 3, No. 3-4, pp. 249-449, 2010.
 E. MolavianJazi and J. N. Laneman. “A finite blocklength perspective on Gaussian multi-access channels”, CoRR, abs/1309.2343, 2013.
 J.-M. Gorce, H. Vincent Poor, J.-M. Kelif, “Spatial Continuum Extensions of Asymmetric Gaussian Channels (Multiple Access and Broadcast)”, https://hal.inria.fr/hal-01265184
The candidate should have earned an MSc degree, or equivalent, in one of the following field: information theory, signal processing, electrical engineering, applied mathematics. He should have a strong background in probabilities and information theory as well as in signal processing for wireless communications. The candidate should be familiar with Matlab and C/C++ languages.
Asymptotic and non-asymptotic information theory, second-order rate, probabilities, mutual information, measure theory, Poisson point process, alpha-stable.
(c) GdR 720 ISIS - CNRS - 2011-2015.