A Unified Framework for One-Shot Achievability via the Poisson Matching Lemma

• Published in: IEEE transactions on information theory Vol. 67; no. 5; pp. 2624 - 2651
• Main Authors: Li, Cheuk Ting, Anantharam, Venkat
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: broadcast channels; Channels; channels with state; Coders; Codes; Coding; Decoding; Distortion measurement; Error analysis; Extraterrestrial measurements; finite-blocklength analysis; Information theory; joint source-channel coding; Matching; Measurement uncertainty; Multiple access; One-shot achievability; Q measurement; Random variables; Representations; Source coding
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2021.3058842

We introduce a fundamental lemma called the Poisson matching lemma, and apply it to prove one-shot achievability results for various settings, namely channels with state information at the encoder, lossy source coding with side information at the decoder, joint source-channel coding, broadcast channels, distributed lossy source coding, multiple access channels and channel resolvability. Our one-shot bounds improve upon the best known one-shot bounds in most of the aforementioned settings (except multiple access channels and channel resolvability, where we recover bounds comparable to the best known bounds), with shorter proofs in some settings even when compared to the conventional asymptotic approach using typicality. The Poisson matching lemma replaces both the packing and covering lemmas, greatly simplifying the error analysis. This paper extends the work of Li and El Gamal on Poisson functional representation, which mainly considered variable-length source coding settings, whereas this paper studies fixed-length settings, and is not limited to source coding, showing that the Poisson functional representation is a viable alternative to typicality for most problems in network information theory.