The half a bit loss of robust source/channel codebooks

We consider the problem of choosing robust codebooks for rate-distortion relative to difference distortion measures, and for capacity-cost relative to additive noise channels. We define an information theoretic formula for the min-max redundancy associated with robust random source codes, and similarly for the loss of robust random channel codes. We then show that this min-max performance can be approached by structured, dithered lattice codebooks. Applications to coding with side information are discussed.