Deterministic Compression with Uncertain Priors

Abstract

Communication in “natural” settings, e.g., between humans, is distinctly different from that in classical designed settings, in that the former is invariably characterized by the sender and receiver not being in perfect agreement with each other. Solutions to classical communication problems thus have to overcome an extra layer of uncertainty introduced by this lack of prior agreement. One of the classical goals of communication is compression of information, and in this context lack of agreement implies that sender and receiver may not agree on the “prior” from which information is being generated. Most classical mechanisms for compressing turn out to be non-robust when sender and receiver do not agree on the prior. Juba et al. (Proc. ITCS 2011) showed that there do exists compression schemes with shared randomness between sender and receiver that do not share a prior that can compress information down roughly to its entropy. In this work, we explore the assumption of shared randomness between the sender and receiver and highlight why this assumption is problematic when dealing with natural communication. We initiate the study of deterministic compression schemes amid uncertain priors, and expose some of the mathematical facets of this problem. We show some non-trivial deterministic compression schemes, and some lower bounds on natural classes of compression schemes. We show that a full understanding of deterministic communication turns into challenging (open) questions in graph theory and communication complexity.