On Asymptotically Optimal Stationary Source Codes for IID Sources

A vector extension of a necessary condition for asymptotically optimal stationary (sliding-block) source codes is presented. The condition implies the intuitive result that the reproduction process for an IID input must be approximately uncorrelated if the code is approximately optimal, a property previously demonstrated empirically for common examples. One-bit coding of a Gaussian IID process is used to illustrate the goodness of fit of the empirical distribution of the reproduction to the Shannon optimal distribution.