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Resolvability on Continuous Alphabets

: Frey, M.; Bjelakovic, I.; Stanczak, S.


Institute of Electrical and Electronics Engineers -IEEE-; IEEE Information Theory Society:
IEEE International Symposium on Information Theory, ISIT 2018 : 17th - 22nd June 2018, Vail, CO, USA
Piscataway, NJ: IEEE, 2018
ISBN: 978-1-5386-4781-3
International Symposium on Information Theory (ISIT) <2018, Vail/Colo.>
Fraunhofer HHI ()

We characterize the resolvability region for a large class of point-to-point channels with continuous alphabets. In our direct result, we prove not only the existence of good resolvability codebooks, but adapt an approach based on the Chernoff-Hoeffding bound to the continuous case showing that the probability of drawing an unsuitable codebook is doubly exponentially small. For the converse part, we show that our previous elementary result carries over to the continuous case easily under some mild continuity assumption.