Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 68, Issue 7, Pages 4224-4229Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2022.3159132
Keywords
Entropy; information theory; entropy power; Schrodinger problem; heat equation
Funding
- Fondation Sciences Mathematiques de Paris (FSMP)
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The aim of this note is to generalize Costa's concavity theorem by studying Shannon's entropy power along entropic interpolations. We provide two proofs with independent interest: one using G-calculus, applicable to more abstract frameworks; the other with an explicit remainder term, similar to Villani's work, allowing us to characterize the case of equality.
Aim of this short note is to study Shannon's entropy power along entropic interpolations, thus generalizing Costa's concavity theorem. We shall provide two proofs of independent interest: the former by G-calculus, hence applicable to more abstract frameworks; the latter with an explicit remainder term, reminiscent of Villani (IEEE Trans. Inf. Theory, 2006), allowing us to characterize the case of equality.
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