List Decoding Random Euclidean Codes and Infinite Constellations

Zhang, Yihan and Vatedka, Shashank (2022) List Decoding Random Euclidean Codes and Infinite Constellations. IEEE Transactions on Information Theory. p. 1. ISSN 0018-9448

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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 and respectively, the list decoding capacity is equal to 1/2log. Random spherical codes achieve constant 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 conjecture that originates in analytic number theory is true, then the list size grows as a polynomial function of the gap-to-capacity. IEEE

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IITH Creators:
IITH CreatorsORCiD
Vatedka, Shashankhttps://orcid.org/0000-0003-2384-9392
Item Type: Article
Uncontrolled Keywords: Codes; Decoding; Integrated circuits; Lattices; Receivers; Transmitters; Upper bound
Subjects: Electrical Engineering
Divisions: Department of Electrical Engineering
Depositing User: . LibTrainee 2021
Date Deposited: 25 Jul 2022 10:24
Last Modified: 25 Jul 2022 10:24
URI: http://raiith.iith.ac.in/id/eprint/9915
Publisher URL: http://doi.org/10.1109/TIT.2022.3189542
OA policy: https://v2.sherpa.ac.uk/id/publication/3480
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