Details

Autor(en) / Beteiligte

• Liu, Jingbo
• Courtade, Thomas A.
• Cuff, Paul
• Verdu, Sergio

Titel

Smoothing Brascamp-Lieb Inequalities and Strong Converses of Coding Theorems

Ist Teil von

• IEEE transactions on information theory, 2020-02, Vol.66 (2), p.704-721

Ort / Verlag

New York: IEEE

Erscheinungsjahr

2020

Quelle

IEEE Xplore

Beschreibungen/Notizen

• The Brascamp-Lieb inequality in functional analysis can be viewed as a measure of the "uncorrelatedness" of a joint probability distribution. We define the smooth Brascamp-Lieb (BL) divergence as the infimum of the best constant in the Brascamp-Lieb inequality under a perturbation of the joint probability distribution. An information spectrum upper bound on the smooth BL divergence is proved, using properties of the subgradient of a certain convex functional. In particular, in the i.i.d. setting, such an infimum converges to the best constant in a certain mutual information inequality. We then derive new single-shot converse bounds for the omniscient helper common randomness generation problem and the Gray-Wyner source coding problem in terms of the smooth BL divergence, where the proof relies on the functional formulation of the Brascamp-Lieb inequality. Exact second-order rates are thus obtained in the stationary memoryless and nonvanishing error setting. These offer rare instances of strong converses/second-order converses for continuous sources when the rate region involves auxiliary random variables.