A Class of Subadditive Information Measures and their Applications
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866909997767589888 |
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| author | Abin, Hamidreza Zinati, Mahdi Gohari, Amin Yassaee, Mohammad Hossein Mojahedian, Mohammad Mahdi |
| author_facet | Abin, Hamidreza Zinati, Mahdi Gohari, Amin Yassaee, Mohammad Hossein Mojahedian, Mohammad Mahdi |
| contents | 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 Csiszár'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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_15639 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Class of Subadditive Information Measures and their Applications Abin, Hamidreza Zinati, Mahdi Gohari, Amin Yassaee, Mohammad Hossein Mojahedian, Mohammad Mahdi Information Theory 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 Csiszár'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. |
| title | A Class of Subadditive Information Measures and their Applications |
| topic | Information Theory |
| url | https://arxiv.org/abs/2601.15639 |