A short proof of the Gács--Körner theorem

2023/06/26 by László Csirmaz, Csirmaz, Laszlo
Decision Sciences · Mathematics · #94A15 #94A24 #94A24 94A15 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2306.14718

openalex publication_date 2023/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a short proof of a celebrated result of Gács and Körner giving sufficient and necessary condition on the joint distribution of two discrete random variables X and Y for the case when their mutual information matches the extractable (in the limit) common information. Our proof is based on the observation that the mere existence of certain random variables jointly distributed with X and Y can impose restriction on all random variables jointly distributed with X and Y.

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