One-Shot Information Theory via the Pairwise Error Probability: Lossy, Joint Source-Channel, Erasure, and Multiuser Coding

Abstract

This paper extends a one-shot (finite-blocklength) information-theoretic framework built on a single primitive: the pairwise error probability (PEP) of a randomized, dither-broken decoding rule, and the error spectrum it induces. A companion paper developed the framework for point-to-point channel coding -- uniformity of the PEP, the error-spectrum representation of achievability and converse, and the linear-programming form of the prior-optimized minimax meta-converse. Here we show that the same primitive, read on an enlarged candidate space, governs four further settings: lossy source coding under average distortion, joint source-channel coding with list decoding, channel coding with an erasure/undetected-error option, and the two-user multiple-access channel. In each case a single spectrum yields a random-coding achievability bound and exact fixed-code identities, and we indicate how the convex -- indeed linear-programming -- prior optimization of the channel-coding case extends under matched decoding. The development recovers the one-shot lossy bound of Matsuta-Uyematsu and the joint source-channel bounds in the Csiszar tradition, complements the lossy bounds of Kostina-Verdu, and connects the multiuser case to the comparable achievability/converse pair through three pairwise error events.