Testing the Isotropic Cauchy Hypothesis.

The isotropic Cauchy distribution is a member of the central α-stable family that plays a role in the set of heavy-tailed distributions similar to that of the Gaussian density among finite second-moment laws. Given a sequence of observations, we are interested in characterizing the performance of Likelihood Ratio Tests, where two hypotheses are plausible for the observed quantities: either isotropic Cauchy or isotropic Gaussian. Under various setups, we show that the probability of error of such detectors is not always exponentially decaying with , with the leading term in the exponent shown to be logarithmic instead, and we determine the constants in that leading term.

Time-Limited Codewords over Band-Limited Channels: Data Rates and the Dimension of the W-T Space.

We consider a communication system whereby -seconds time-limited codewords are transmitted over a -Hz band-limited additive white Gaussian noise channel. In the asymptotic regime as WT→∞, it is known that the maximal achievable rates with such a scheme converge to Shannon's capacity with the presence of 2WT degrees of freedom. In this work we study the degrees of freedom and the achievable information rates for finite values of WT.