On the redundancy of lossy source coding with abstract alphabets

作     者：Yang, E Zhang, Z 

作者机构：Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada Univ So Calif Dept Elect Engn Syst Inst Commun Sci Los Angeles CA 90089 USA 

出 版 物：《IEEE TRANSACTIONS ON INFORMATION THEORY》 (IEEE Trans. Inf. Theory)

年 卷 期：1999年第45卷第4期

页      面：1092-1110页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：National Sciences Foundation, (NCR 9508282, NCR 9805312) Natural Sciences and Engineering Research Council of Canada, NSERC, (RGPIN203035-98) University of Waterloo 

主　　题：data compression lossy source coding random coding argument rate distortion (distortion rate) function redundancy 

摘      要：The redundancy problem of lossy source coding with abstract source and reproduction alphabets is considered. 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}(n=1)(infinity) of block codes at the rate R such that the distortion redundancy of C-n (defined as the difference between the performance of C-n and the distortion rate function d(P, R) of P] is upper-bounded by \partial derivative d(P, R)/partial derivative R\ ln n/2n + o (In n/n), For coding at a fixed distortion level, it is demonstrated that for any d 0 and any memoryless abstract alphabet source P satisfying some mild conditions, there exists a sequence {C-n}(n=1)(infinity) of block codes at the fixed distortion d such that the rate redundancy of C-n, (defined as the difference between the performance of C-n and the rate distortion function R(P, d) of P) is upper-bounded by (7 ln n)/(6n) + o(ln n/n). 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 of memoryless Gaussian sources.