Technical Program

Paper Detail

Paper Title List Decoding Random Euclidean Codes and Infinite Constellations
Paper IdentifierWE2.R4.5
Authors Yihan Zhang, The Chinese University of Hong Kong, Hong Kong SAR of China; Shashank Vatedka, Telecom ParisTech, France
Session Lattice Codes
Location Odéon, Level 3
Session Time Wednesday, 10 July, 11:40 - 13:20
Presentation Time Wednesday, 10 July, 13:00 - 13:20
Manuscript  Click here to download the manuscript
Abstract We study the list decodability of different ensembles of codes over the real alphabet under the assumption of an omniscient adversary. It is a well-known result that when the source and the adversary have power constraints $ P $ and $ N $ respectively, the list decoding capacity is equal to $ \frac{1}{2}\log\frac{P}{N} $. Random spherical codes achieve capacity with constant (as a function of the blocklength) list sizes, and the goal of the present paper is to obtain a better understanding of the smallest achievable list size as a function of the gap to capacity. We show a reduction from arbitrary codes to spherical codes, and derive a lower bound on the list size of typical random spherical codes. We also give an upper bound on the list size achievable using nested Construction-A lattices and infinite Construction-A lattices. We then define and study a class of infinite constellations that generalize Construction-A lattices and prove upper and lower bounds for the same. Other goodness properties such as packing goodness and AWGN goodness of infinite constellations are proved along the way. Finally, we consider random lattices sampled from the Haar distribution and show that if a certain number-theoretic conjecture is true, then the list size grows as a polynomial function of the gap-to-capacity.