Guessing under source uncertainty

TL;DR

This paper addresses the problem of guessing a source's realization with side information when the source belongs to an uncertain family, introducing new divergence measures and strategies to minimize worst-case redundancy.

Contribution

It introduces a novel divergence measure with Pythagorean property and characterizes optimal guessing strategies under source uncertainty.

Findings

Redefines redundancy for source guessing with side information.

Identifies optimal strategies minimizing worst-case redundancy.

Determines redundancy bounds for specific source families.

Abstract

This paper considers the problem of guessing the realization of a finite alphabet source when some side information is provided. The only knowledge the guesser has about the source and the correlated side information is that the joint source is one among a family. A notion of redundancy is first defined and a new divergence quantity that measures this redundancy is identified. This divergence quantity shares the Pythagorean property with the Kullback-Leibler divergence. Good guessing strategies that minimize the supremum redundancy (over the family) are then identified. The min-sup value measures the richness of the uncertainty set. The min-sup redundancies for two examples - the families of discrete memoryless sources and finite-state arbitrarily varying sources - are then determined.