Breakdown of a concavity property of mutual information for non-Gaussian channels
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Date
2024-06Type
- Journal Article
ETH Bibliography
yes
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Abstract
Let S and S̃ be two independent and identically distributed random variables, which we interpret as the signal, and let P1 and P2 be two communication channels. We can choose between two measurement scenarios: either we observe S through P1 and P2, and also S̃ through P1 and P2; or we observe S twice through P1, and S̃ twice through P2. In which of these two scenarios do we obtain the most information on the signal (S, S̃)? While the first scenario always yields more information when P1 and P2 are additive Gaussian channels, we give examples showing that this property does not extend to arbitrary channels. As a consequence of this result, we show that the continuous-time mutual information arising in the setting of community detection on sparse stochastic block models is not concave, even in the limit of large system size. This stands in contrast to the case of models with diverging average degree, and brings additional challenges to the analysis of the asymptotic behavior of this quantity. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000668719Publication status
publishedExternal links
Journal / series
Information and Inference: A Journal of the IMAVolume
Pages / Article No.
Publisher
Oxford University PressSubject
information theory; mutual information; stochastic block modelRelated publications and datasets
Is new version of: http://hdl.handle.net/20.500.11850/644284
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ETH Bibliography
yes
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