Bayesian Asymptotics: From Universal Source Coding to General Large-Scale MIMO Communication
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In this talk, I will first provide a brief overview of the role of Bayesian asymptotics in universal source coding, specifically through mixture codes such as the well-known Krichevsky-Trofimov coding distribution for i.i.d. sources and the context-tree weighting algorithm for variable-order Markov sources. I will then transition to the large-scale MIMO communication problem by connecting the minimum Bayesian redundancy in source coding to the maximum mutual information in channel coding. Specifically, I will demonstrate that the asymptotic capacity of a general MIMO channel, under both peak and average power constraints, admits a simple and elegant expression through what we term the Jeffreys factor, with the optimal input distribution being the tilted Jeffreys prior.
Finally, I will provide a systematic three-step recipe to compute this asymptotic capacity and apply it to diverse scenarios such as channels with clipping, phase noise, output quantization, fading channels with imperfect channel knowledge, and optical Poisson channels. If time permits, I will conclude with a discussion on constellation design for large-scale MIMO channels.
Keywords: Bayesian Asymptotics, Universal Source Coding, MIMO Communications, Information Theory, Channel Capacity, Wireless Communications.
Prof. Sheng Yang received the B.E. degree in Electrical Engineering from Jiaotong University, Shanghai, China, in 2001, and both the Engineer degree and M.Sc. degree in Electrical Engineering from Telecom Paris, France, in 2004. He obtained his Ph.D. from Universite Pierre et Marie Curie (Paris VI) in 2007.
Since December 2008, he has joined CentraleSupelec, Paris-Saclay University, where he is currently a Full Professor. He has also held visiting professorships at the University of Hong Kong and HKUST. He received the 2015 IEEE ComSoc Young Researcher Award for the Europe, Middle East, and Africa Region (EMEA). He was an Associate Editor of IEEE Transactions on Wireless Communications from 2015 to 2020 and has been an Associate Editor of IEEE Transactions on Information Theory since 2021.