Number Theory and Communications


The reading group will take place in Room 909a, normally on Tuesdays 14:15-16:00 . This is an informal reading group, where each volunteer presents a topic based on a recent paper or a book chapter. The word "Communications" is understood broadly, as to include applications in cryptography, signal processing, etc. 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
04/10 Algebraic Number Theory: Motivation and Fundamental Results
based on [1], Ch. 5,6 and [2]
Antonio Campello
07/10
(Friday 10:00-12:00)		 Compute-and-Forward and Integer Forcing Shanxiang Lyu and William Liu
11/10 Division Algebras for MIMO Channels
based on [3] 		Antonio Campello
25/10 Maximal Orders
based on [4] 		Charles Grover
01/11 Partition Chains of Ideal Lattices Ling Liu
08/11 The Principal Ideal Problem
based on [5-6] 		Charles Grover
15/11 Non-Principal Ideals and Reciprocity Laws
based on [7], Ch. 6 and [8]		 Cong Ling
22/11 Extracting Wyner's Common Information Using
Polar Codes and Polar Lattices [9-10]		 Jinwen Shi
29/11 Quaternion-Valued Signal-Processing
based on [12] and [13] 		Min Xiang
06/12 Gaussian comparison lemma and convex optimisation [11] Shanxiang Lyu

Suplementary bibliography

[1] F. Oggier and E. Viterbo. Algebraic Number Theory and Code Design for Rayleigh Fading Channels. Foundations and Trends in Communications and Information Theory, NOW, 1(3):333-416, 2004. (link)
[2] P. Samuel. Algebraic Theory of Numbers. Translated by Allan J. Silberger. Mineola, NY: Dover, 2008
[3] P. Elia, K. Raj Kumar, S. A. Pawar, P. Vijay Kumar and H.-F. Lu, "Explicit, Minimum-Delay Space-Time Codes Achieving The Diversity-Multiplexing Gain Tradeoff," IEEE Transactions on Information Theory, 52(9):3869-3884, 2006.(link)
[4] I. Reinert. Maximal Orders. Academic Press, New York, 1975
[5] J.-F. Biasse and F. Song, On the quantum attacks against schemes relying on the hardness of finding a short generator of an ideal in Q(\zeta_pn), 2015 (link)
[6] R. Cramer et al. Recovering Short Generators of Principal Ideals in Cyclotomic Rings, (link)
[7] R. A. Mollin, Algebraic Number Theory, 2nd ed. CRC Press, 2011
[8] R. Cramer, L. Ducas and B. Wesolowski, Short Stickelberger Class Relations and application to Ideal-SVP, 2016 (link)
[9] R. Gray and A. Wyner, "Source coding for a simple network," Bell System Technical Journal, vol. 53, no. 9, pp. 1681-1721, 1974.
[10] G. Xu, W. Liu, and B. Chen, "A lossy source coding interpretation of Wyner's common information," IEEE Trans. Inf. Theory, vol. 62,pp. 754-768, 2016.
[11] C. Thrampoulidis, S. Oymak and B. Hassibi, "The Gaussian min-max theorem in the Presence of Convexity", 2014 (link)
[12] J. P. Ward, Quaternions and Cayley numbers: Algebra and applications. Vol. 403. Springer Science & Business Media, Dordrecht, The Netherlands, 2012.
[13] J. Via, D. Ramirez, and I. Santamaria, "Properness and widely linear processing of quaternion random vectors," IEEE Trans. Inf. Theory, vol. 56, no. 7, pp. 3502-3515