Maximin performance of binary-input channels with uncertain noise distributions

Abstract

Abstract-We consider uncertainty classes of noise distributions defined by a bound on the divergence with respect to a nominal noise distribution. The noise that maximizes the minimum error probability for binary-input channels is found. The effect of the reduction in uncertainty brought about by knowledge of the signal-to-noise ratio is also studied. The particular class of Gaussian nominal distributions provides an analysis tool for nearGaussian channels. Asymptotic behavior of the least favorable noise distribution and resulting error probability are studied in a variety of scenarios, namely: asymptotically small divergence with and without power constraint; asymptotically large divergence with and without power constraint; and asymptotically large signal-to-noise ratio.Index Terms-Detection, Gaussian error probability, hypothesis testing, Kullback-Leibler divergence, least favorable noise.

Robust Hypothesis Testing With a Relative Entropy Tolerance

“…The problem (2.6) is also closely related to the worst-case noise detection problem considered in [11], where for hypotheses…”

“…Thus the problem (2.6) differs from the one examined in [10], [11] by the fact that we allow the least-favorable noise distribution to be different under hypotheses H 0 and H 1 , instead of insisting they should be the same.…”

“…Thus the difference between the problem we consider and [11] is that we allow the additive noise statistics to be different under each hypothesis, instead of forcing them to be the same. Finally, it is worth noting that [12] also examines robust hypothesis testing by using the relative entropy as a mismatch metric between actual and nominal densities, but it does so asymptotically as the number of measurements becomes infinite, so its results take a very different form.…”

On the Equivalence of <tex>$f$</tex>-Divergence Balls and Density Bands in Robust Detection

“…A common way of specifying uncertainty sets is via a neighborhood around a nominal distribution, which represents an ideal system state or model [2]. In many works on robust detection, the use of f -divergence balls has been proposed as a useful and versatile model to construct such neighborhoods [3][4][5][6][7][8][9][10]. In contrast to outlier models, such as ε-contamination [11], f -divergence balls do not allow for arbitrarily large deviations from the nominals and, therefore, have been argued to better represent scenarios where the shape of a distribution is subject to uncertainty, but there are no gross outliers in the data [5].…”

Adaptive multicoding and robust linear-quadratic receivers for uncertain CDMA frequency-selective fading channels

“…For example, in [61], censoring of data in the frequency domain was used to reduce the sensitivity of detector performance to unknown narrowband interference. Also, in [62,63], McKellips and Verdu study the characterization and impact of uncertain noise distribution and worst-case additive noise distribution with respect to maximum probability of error under power and divergence constraints.…”