##### Title

Non-asymptotic fundamental limits of impulsive radio communications

##### Laboratory

CITI Lab. Centre of Innovation in Telecommunications and Integration of Service (www.citilab.fr)

##### Funding

This PhD position takes part of the ANR project ARBurst that has been submitted to the ANR2015. The position will be fully funded if the project is accepted. The final answer for the funding will be known in July 2015.

##### Contacts

Prof. Jean-Marie Gorce

perso.citi.insa-lyon.fr/jmgorce

Dr. Philippe Mary

##### 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, 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 M2M networks based on the non-asymptotic information theory framework [1] but taking into account bursty communications, i.e. use of non-Gaussian interference distribution [2], and large-scale deployment, i.e. use of stochastic geometry tool [3]. The candidate will first address the problem of the non-asymptotic bounds (achievability and converse) 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 κβ bound method for the achievability part. One the challenge would be to derive an expression (or compute) the dispersion of the impulsive channel [1]. The MolavianJazi’s method [4], based on the central limit theorem (CLT) for functions, could also be investigated in order to approach the mutual information density for a stable noise. The inherent dependence between the rate and the error-probability in finite blocklength regime will help us to define a multiobjective framework for the evaluation of the M2M network performances. Based on these results, the PhD candidate will extend the previous approach to the multi-user case, through the study of the multiple access channel (MAC) and broadcast channel (BC). Based on the outage-splitting theorem for Gaussian MAC [4], the candidate will address the problem of the achievable region of MAC in impulsive noise. The BC scenario will be investigated as a next step. Generally, i.e. in Gaussian framework, the achievable region of multi-user communications is derived under finite second-order moment. This assumption does not hold generally 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 M2M context. Finally, interfering users will be considered as (non-gaussian) noise, but distributed as a Poisson point process (PPP). The challenge is to merge the non-asymptotic theory to the stochastic geometry tool in order to figure out how the channel dispersion behaves in a randomly deployed network and when the interference is considered as non-Gaussian. 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.

##### Key skills

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.

##### Key words

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

##### 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 MSc)

– 2 or 3 references

– Deadline for application September 15th, 2016

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

[3] 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.

[4] E. MolavianJazi and J. N. Laneman. “A finite blocklength perspective on Gaussian multi-access channels”, CoRR, abs/1309.2343, 2013.