Multiple packing is a natural generalization of sphere packing . We revisit the problem of high-dimensional multiple packing in Euclideanspace . We study the multiplepacking problem for both bounded point sets and unbounded point sets . We derive various bounds on the largest possible density of a multiple packing . A related notion called average-radiusmultiple packing is also studied . Some of our lower bounds pin down theasymptotics of certain ensembles of average- radius list-decodable codes, e.g.,(expurgated) Gaussian codes and Poisson Point Processes . To thisend, we apply tools from geometry and large deviation theory to thisend of the problem . We use tools from high-dimension geometry and other large deviation theories to find out what the error exponent is of independent interest beyond multiple packings are of interest beyond the multiple packing theory . For more information, please visit http://www.mailonline.com/dailymailonline/news/science-news/2014/article-article-report-to-the-paper-and-cheating-research-report/chilling-research/chillboard/chiller-chillboarding-chilling/blinding-blowing-blipping-blitting-blitching-blacking-blick-blurring-blissing-blusing-blushing-blanking-blinding

Author(s) : Yihan Zhang, Shashank Vatedka

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Keywords : packing - multiple - bounds - problem - point -

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