An Asymptotically Optimal Transform of Pearson’s Correlation Statistic

Sequence pairs with asymptotically optimal aperiodic correlation

The Pursley-Sarwate criterion of a pair of finite complex-valued sequences measures the collective smallness of the aperiodic autocorrelations and the aperiodic crosscorrelations of the two sequences. It is known that this quantity is always at least 1 with equality if and only if the sequence pair is a Golay pair. We exhibit pairs of complex-valued sequences whose entries have unit magnitude f...

Asymptotically Optimal Deterministic Rendezvous

In this paper, we address the deterministic rendezvous in graphs where k mobile agents, disseminated at different times and different nodes, have to meet in finite time at the same node. The mobile agents are autonomous, oblivious, labeled, and move asynchronously. Moreover, we consider an undirected anonymous connected graph. For this problem, we exhibit some asymptotical time and space lower ...

Asymptotically optimal Boolean functions

The largest Hamming distance between a Boolean function in $n$ variables and the set of all affine Boolean functions in $n$ variables is known as the covering radius $\rho_n$ of the $[2^n,n+1]$ Reed-Muller code. This number determines how well Boolean functions can be approximated by linear Boolean functions. We prove that \[ \lim_{n\to\infty}2^{n/2}-\rho_n/2^{n/2-1}=1, \] which resolves a conj...

An Optimal Property of the Likelihood Ratio Statistic

Asymptotically optimal block quantization

for the mean-square quantizing error where N is the. number of level&p(x) is the probability density of the input, and E’(x) is the slope of the compressor curve. The formula, an approximation based on the assumption that the number of levels is large and overI& distortion is negligible, is a useful tool for analytical studies of quantfzation. This paper gives a bedstlc argument generallhg Beme...