High rate mismatch in entropy constrained quantization

It is shown that if an asymptotically optimal sequence of variable rate codes is designed for a k-dimensional probability density function (pdf) g and then applied to another pdf f for which f/g is bounded, then the resulting mismatch or loss of performance from the optimal possible is given by the relative entropy or Kullback-Leibler divergence I(f/spl par/g). It is also shown that under the same assumptions an asymptotically optimal code sequence for g can be converted to an asymptotically optimal code sequence for a mismatched source f by modifying only the lossless component of the code. The development does not require Gersho´s conjecture.