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Number Theory and Communications- Fall, 2016

Emerging Coding Techniques

Major telecommunications companies are on the run for the standardization of the codes and protocols for the new 5G technology, to be released in 2020. Following this trend, the reading group of this semester will mostly focus on new mathematical tools (or old ones, revisited in a new context) for coding. The preference is for constructive coding techniques, which may a technological impact in the near future. Each exposition is intended to explain, in sufficient detail, the main idea of one major emerging coding technique. As usual, blackboard talks are most appreciated.

This is an informal reading group, where each volunteer presents a topic based on a recent paper or a book chapter.
The reading group will take place in Room 503, usually on Mondays 14:00-15:30 . If you want to give a talk or propose a new topic, drop me an e mail (a.campello@imperial.ac.uk).

Schedule

Date Topic Reader
06/02
13/03
Codes for Caching
based on [1]
Nitish Mital
13/02 Codes for Cloud Storage
based on [2]
Antonio Campello
20/02 Codes for Gaussian Relay Networks
Degrees-of-freedom and diophantine approximations, based on [3]
Shanxiang Lyu
27/02 Polar codes for 5G
Based on [4,5]
Jinwen Shi
06/03 Quantum Polar Codes
Based on [6]
Jiabo Wang
13/03 Codes for the Multiple-Access Channel 1
based on [7]
Cong Ling
20/03 Codes for the Multiple-Access Channel 2
based on [8]
Antonio Campello
27/03 Reed-Muller Codes
Capacity-Achieving in the BEC
Ling Liu
03/04 LWE over Division Algebras Charlie Grover

Suplementary bibliography

[1] Maddah-Ali, M. and Niesen, U. "Fundamental Limits of Caching", IEEE Transactions on Information Theory, 2014 (links here or here)
[2] Dimakis et al. "Network Coding for Distributed Storage Systems", IEEE Transactions on Information Theory 2010, (link)
[3] Niesen, U., & Whiting, P. The degrees of freedom of compute-and-forward. IEEE Transactions on Information Theory, 2012. (link)
[4-5] "Minimum-Distance Based Construction of Multi-Kernel Polar Codes" and "Multi-Kernel Construction of Polar Codes" (links here and here).
[6] Mark M. Wilde, Saikat Guha, "Polar Codes for Classical-Quantum Channels", IEEE Transactions on Information theory, 2013. (link)
[7] D. Tse, P. Viswanath and L. Zheng, Diversity-Multiplexing Tradeoff in Multiple Access Channels, IEEE Transactions on Information Theory, 2004. (link)
[8J J. Zhu and M. Gastpar, "Gaussian Multiple Access via Compute-and-Forward," in IEEE Transactions on Information Theory, 2016 (link)