Tight Bounds for Symmetric Divergence Measures and a Refined Bound for Lossless Source Coding

Abstract

Tight bounds for several symmetric divergence measures are derived in terms of the total variation distance. It is shown that each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these bounds for lossless source coding is provided, refining and improving a certain bound by Csiszár. Another application of these bounds has been recently introduced by Yardi. et al. for channel-code detection.

Appears in the IEEE Trans. on Information Theory, February 2015. arXiv admin note: substantial text overlap with arXiv:1502.06428

References in corpus (1)

• Properties of Classical and Quantum Jensen-Shannon Divergence

Cited by in corpus (5)

• $f$-divergence Inequalities
• On $f$-Divergences: Integral Representations, Local Behavior, and Inequalities
• Maximally Consistent Sampling and the Jaccard Index of Probability Distributions
• Tight Bounds for Symmetric Divergence Measures and a New Inequality Relating $f$-Divergences
• Proximity Operators of Discrete Information Divergences