High-SNR Asymptotics of Mutual Information for Discrete Constellations With Applications to BICM
Dr. Alex Alvarado
Optical Networks Group,
Department of Electronic & Electrical Engineering,
University College London
Abstract:
Asymptotic expressions of the mutual information between any discrete input and the corresponding output of the scalar additive white Gaussian noise channel are presented in the limit as the signal-to-noise ratio (SNR) tends to infinity. Asymptotic expressions of the symbol-error probability (SEP) and the minimum mean-square error (MMSE) achieved by estimating the channel input given the channel output are also developed. It is shown that for any input distribution, the conditional entropy of the channel input given the output, MMSE, and SEP have an asymptotic behavior proportional to the Gaussian Q-function. The argument of the Q-function depends only on the minimum Euclidean distance (MED) of the constellation and the SNR, and the proportionality constants are functions of the MED and the probabilities of the pairs of constellation points at MED. The developed expressions are then generalized to study the high-SNR behavior of the generalized mutual information (GMI) for bit-interleaved coded modulation (BICM). By means of these asymptotic expressions, the long-standing conjecture that Gray codes are the binary labelings that maximize the BICM-GMI at high SNR is proven. It is further shown that for any equally spaced constellation whose size is a power of two, there always exists an anti-Gray code giving the lowest BICM-GMI at high SNR.
Biography:
Alex Alvarado was born in 1982 in Quellón, on the island of Chiloé, Chile. He obtained his Electronic Engineering Diploma (Ingeniero Civil Electrónico) and his Master of Science in Electronic Engineering (Magíster en Ciencias de la Ingeniería Electrónica) from the Departamento de Electrónica, Universidad Técnica Federico Santa María (UTFSM), Chile, in 2003 and 2005, respectively. During 2006 he was a research intern at Institut national de la recherche scientifique, Énergie, Matériaux et Télécomunications (INRS&EMT), Montreal Canada. He obtained the degree of Licentiate of Engineering (Teknologie Licentiatexamen) in 2008 and his PhD degree in 2011, both of them from Chalmers University of Technology, Gothenburg, Sweden.
Dr. Alvarado is currently a Senior Research Associate at the Optical Networks Group, University College London, United Kingdom. In 2012-2014 he was a Marie Curie Intra-European Fellow at the University of Cambridge, United Kingdom, and during 2011-2012 he was a Newton International Fellow at the same institution. In 2008, he was holder of the Merit Scholarship Program for Foreign Students, granted by the Ministère de l'Éducation, du Loisir et du Sports du Québec and during 2012-2014, he was also a Research Associate at Trinity Hall, Cambridge.