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

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 two- or three-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.