Master 2 internship: Performance of polar codes in finite block length regime
Place: Institut d'Electronique et de Télécommunication de Rennes, Rennes France.
Date and duration: start in February - March for a duration about 5 - 6 months.
Keywords: polar codes, coding theory, finite block length information theory.
Supervisor: Philippe Mary, firstname.lastname@example.org
With the recent development of machine-to-machine (M2M) communications and internet-of-things (IoT) networks, the infrastructures have to support a lot of users (or nodes) but each of them requesting a very small quantity of information. The goal of the project ARBurst (https://project.inria.fr/arburst/)aims at providing fundamental bounds for these networks. Among the bunch of characteristics of IoT networks, one can cite short packet communications and impulsive transmissions due to the uncoordinated communication protocols for a such large number of nodes. 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.
On the other hand, polar codes, introduced by Arikan  are the first provable capacity-achieving codes of any discrete memoryless channels when the size of the code goes to infinity . In finite block length, i.e. when the block size remains bounded, the channel polarization is incomplete, leading to noisy sub-channels. Some works have investigated the theoretical performance of polar codes in the finite block length regime , and some practical implementations are even planned for future 5G networks . In addition, the design of good polar codes in additive white Gaussian noise (AWGN) channel is challenging due to the non-universality of these codes in Gaussian noise, i.e. the choice of (good) code strongly depends on SNR .
This internship aims at implementing and evaluating the performance of such codes in AWGN channel in a first step when the number of channel uses remains bounded and in a second step, if the remaining time allows it, investigating the behavior in impulsive noise.
A tentative schedule for the internship would be:
1)State of the art on the polar codes; theory, design and decoding.
2)Implementation of polar codes in AWGN channel and comparison to non-asymptotic bounds.
3)Performance evaluation in additive non-Gaussian noise.
 E. Arikan, “Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels”, IEEE Transactions on Information Theory, vol. 55, no. 7, 2009.
 K. Niu, K. Chen, J. Lin, Q. T. Zhang, “Polar codes : Primary concepts and practical decoding algorithms”, IEEE Communications Magazine, vol. 52, no. 7, 2014.
 D. Goldin, D. Burshtein, “Improved Bounds on the Finite Length Scaling of Polar Codes”, IEEE Transactions on Information Theory, vol. 60, no. 11, 2014.
 V. Bioglio, C. Condo, I. Land, “Design of Polar Codes in 5G New Radio”, https://arxiv.org/pdf/1804.04389.pdf
 H. Vangala, E. Viterbo, Y. Hong, “A comparative study of polar code constructions for the AWGN channel”, https://arxiv.org/pdf/1501.02473.pdf
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. The candidate should be familiar with Matlab and C/C++ languages or Python.
Polar codes, coding theory, asymptotic and non-asymptotic information theory.
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 selected
Dr. Philippe Mary
INSA de Rennes / IETR UMR CNRS – 6164
(c) GdR 720 ISIS - CNRS - 2011-2018.