... Zeger

J. Hamkins (hamkins@jpl.nasa.gov) is with the Jet Propulsion Laboratory, 4800 Oak Grove Dr., Pasadena, CA 91109-8099. K. Zeger (zeger@ucsd.edu) is with the Department of Electrical and Computer Engineering, University of California at San Diego, La Jolla, CA 92093-0407. This work was supported in part by the National Science Foundation and the UCSD Center for Wireless Communications. This paper was presented in part at the IEEE International Symposiums on Information Theory, in Ulm, Germany, July 1997, and in Washington, D.C., June 2001.

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... source

Moo and Neuhoff [36] showed that the minimum MSE for quantizing a non-uniform unbounded source using a lattice, decays to zero asymptotically as $2^{-2R+O(\log(R))}$ instead of the known $2^{-2R + O(1)}$ decay rate using asymptotically optimal quantizers.

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... well.

Paley's Theorem (1933) [47] guarantees that Hadamard matrices exist for orders equal to $n=2^e (p^m+1)$, for all positive integers $e$ and $m$, and every odd prime $p$ (also for $p=0$ when $e\ge 2$). The orders for which Hadamard matrices exist include every multiple of 4 up to 268, and all powers of 2. It is an open question as to whether they exist for orders equal to all multiples of 4.

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