Small Robust Response-Surface Designs for Quantitative and Qualitative Factors

Alphabet Source Coding Theorem Revisited En-hui Yang and Zhen Zhang * University of Waterloo, Ontario CANADA, e-mail: [email protected] **University of Southern California, Los Angeles, CA 90089, USA, [email protected] The abstract alphabet source coding theorem is revisited. For coding at a fixed rate level, it is shown that for any fixed rate R > 0 and any memoryless abstract alphabet source P satisfying some mild conditions, there exists a sequence {Cn} of block codes at the rate R such that the distortion redundancy of Cn (defined as the difference between the performance of Cn and the distortion rate function d (P, R) of P) is upper bounded. For coding at the fixed distortion level, it is demonstrated that for every d > 0 and any memoryless abstract alphabet source P satisfying some mild conditions, there exists a sequence { Cn} of block codes at the fixed distortion d such that the rate redundancy Cn (defined as the difference between the performance of Cn and the rate distortion function R(P, d) of P) is upper bounded. These results strengthen the traditional Berger’s abstract alphabet source coding theorem, and extend the positive redundancy results of Zhang, Yang and Wei on lossy source coding with finite alphabets and the redundancy result of Wyner on block coding memoryless Gaussian sources.