10 janvier 2017

Catégorie : Stagiaire

What : Master research internship on Spatial continuum model for finite block length regime.

Topic: Definition of the dispersion of the broadcast channel (BC) when a continuum of users is used in finite block length regime.

When : From February to July

Where : INSA Lyon / CITI Lab

*Laboratory***:**

**CITI : Centre of Innovations in Telecommunications and Integration of Service**

** Start date : **1st February

*Topic*

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 [1,2], the consequent bursty nature also invalidates the Gaussian assumption usually used to model the interference distribution [3]. As a consequence fundamental limits are neither well known nor even well formulated. **The goal of the internship is to deal with the dispersion of the broadcast channel when a continuum of users is considered [4].** The internship aims at evaluating the achievability bound when a certain source rate of the cell and information packet size to each user have to be provided. Moreover, the users are constraint in delay hence the service has to be completed in n channel uses.

Starting with the achievable region of the degraded broadcast channel in finite block length, a suitable partition of space will be defined in order to define a set feasible networks in finite block length. The dispersion of BC with density of users will be defined and the achievable rate when the partitioning tends to infinity will be asset either theoretically or in simulation.

*References*

[1] 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.

[2] P. Mary, J.-M. Gorce, A. Unsal, H.V. Poor, “Finite Block Length Information Theory: What is the Practical Impact on Wireless Communications”, IEEE Globecom Workshops, IoT-Link, Washington D.C., USA, 2016

[3] G. Samorodnitsky and M. S. Taqqu, *Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance*, Chapmann and Hall, 1994.

[4] 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

*Key skills*

The candidate should apply for 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.

*Key words:*

Asymptotic and non-asymptotic information theory, second-order rate, probabilities, mutual information, measure theory, Poisson point process.

*How to apply:*

- Email a motivation letter
- Full CV with project and courses that could be related to the subject
- Complete academic records (from Bachelor to first year of MSc)
**Applications will be reviewed when they arrive until one candidate is select**

*Contacts:*

Dr. Philippe Mary, INSA de Rennes / IETR UMR CNRS - 6164

philippe.mary@insa-rennes.fr ; http://pmary.perso.insa-rennes.fr

Prof. Jean-Marie Gorce, INSA Lyon / CITI Lab

jean-marie.gorce@insa-lyon.fr

(c) GdR 720 ISIS - CNRS - 2011-2015.