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arXiv · 2601.15639

A Class of Subadditive Information Measures and their Applications

Hamidreza Abin·Mahdi Zinati·Amin Gohari·Mohammad Hossein Yassaee·Mohammad Mahdi Mojahedian
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Abstract

We introduce a two-parameter family of discrepancy measures, termed \emph{$(G,f)$-divergences}, obtained by applying a non-decreasing function $G$ to an $f$-divergence $D_f$. Building on Csisz\'ar's formulation of mutual $f$-information, we define a corresponding $(G,f)$-information measure $ I_{G,f}(X;Y)$. A central theme of the paper is subadditivity over product distributions and product channels. We develop reduction principles showing that, for broad classes of $G$, it suffices to verify divergence subadditivity on binary alphabets. Specializing to the functions $G(x)\in\{x,\log(1+x),-\log(1-x)\}$, we derive tractable sufficient conditions on $f$ that guarantee subadditivity, covering many standard $f$-divergences. Finally, we present applications to finite-blocklength converses for channel coding, bounds in binary hypothesis testing, and an extension of the Shannon--Gallager--Berlekamp sphere-packing exponent framework to subadditive $(G,f)$-divergences.

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Hamidreza Abin, Mahdi Zinati, Amin Gohari, Mohammad Hossein Yassaee, Mohammad Mahdi Mojahedian. 2026-01-22. A Class of Subadditive Information Measures and their Applications. https://arxiv.org/abs/2601.15639

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