146,573 research outputs found
Sharper Upper Bounds for Unbalanced Uniquely Decodable Code Pairs
Two sets form a Uniquely Decodable Code Pair
(UDCP) if every pair , yields a distinct sum , where
the addition is over . We show that every UDCP , with and , satisfies . For sufficiently small , this bound significantly
improves previous bounds by Urbanke and Li~[Information Theory Workshop '98]
and Ordentlich and Shayevitz~[2014, arXiv:1412.8415], which upper bound
by and , respectively, as approaches .Comment: 11 pages; to appear at ISIT 201
Two dimensional Berezin-Li-Yau inequalities with a correction term
We improve the Berezin-Li-Yau inequality in dimension two by adding a
positive correction term to its right-hand side. It is also shown that the
asymptotical behaviour of the correction term is almost optimal. This improves
a previous result by Melas.Comment: 6 figure
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