基于成对错误概率的单样本信息论：有损、联合信源信道、删除及多用户编码
One-Shot Information Theory via the Pairwise Error Probability: Lossy, Joint Source-Channel, Erasure, and Multiuser Coding
AI总结：
本文扩展了基于成对错误概率的单样本信息论框架，将其应用于有损信源编码等四种场景，恢复了相关界并建立了多用户场景与可达性/逆对的关联。
AI中文摘要：
本文扩展了以单一基础要素构建的单样本（有限块长）信息论框架，该要素为随机抖动解码规则的成对错误概率（PEP）及其诱导的误差谱。配套论文已开发了该框架用于点对点信道编码的情况，包括PEP的一致性、可达性与逆的误差谱表示，以及先验优化极小极大元逆的线性规划形式。本文表明，在扩大的候选空间上应用同一基础要素，可支配另外四种场景：平均失真下的有损信源编码、带列表译码的联合信源信道编码、带有删除/未检测错误选项的信道编码，以及两用户多址信道。每种场景中，单一谱可产生随机编码可达性界和精确的固定码恒等式，且本文说明信道编码场景下的凸性（实为线性规划）先验优化如何在匹配译码下扩展。该推导恢复了Matsuta-Uyematsu的单样本有损界和Csiszar传统中的联合信源信道界，补充了Kostina-Verdu的有损界，并通过三个成对错误事件将多用户场景与可比的可达性/逆对关联起来。
英文摘要：
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.
