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We formalize the tail redundancy of a collection ${\mathcal{ P}}$ of distributions over a countably infinite alphabet, and show that this fundamental quantity characterizes the asymptotic per-symbol minimax redundancy of universally compressing sequences generated i.i.d. from ${\mathcal{ P}}$ . Contrary to the worst case formulations of universal compression, finite single letter minimax (average case) redundancy of ${\mathcal{ P}}$ does not automatically imply that the expected minimax redundancy of describing length- $n$ strings sampled i.i.d.

Current methods which compress multisets at an optimal rate have computational complexity that scales linearly with alphabet size, making them too slow to be practical in many real-world settings. We show how to convert a compression algorithm for sequences into one for multisets, in exchange for an additional complexity term that is quasi-linear in sequence length. This allows us to compress multisets of exchangeable symbols at an optimal rate, with computational complexity decoupled from the alphabet size.

In decentralized and decision-oriented communication paradigms, autonomous devices strategically implement information compression policies. In this work, we study a strategic communication game between an encoder and two decoders. An i.i.d. information source, observed by the encoder, is transmitted to the decoders via two perfect links, one reaching the first decoder only and the other reaching both decoders, as in the successive refinement setup.