A UNIFIED APPROACH TO TREE-STRUCTURED AND MULTISTAGE VECTOR QUANTIZATION FOR NOISY CHANNELS

Vector quantization (VQ) is a powerful and effective scheme that is wi dely used in speech and image coding applications. Two basic problems can be associated with VQ: (1) its large encoding complexity, and (2) its sensitivity to channel errors. These two problems have been indepe ndently studied in the past. These two problems are examined jointly. Specifically, the performances of two low-complexity VQ's-the tree-str uctured VQ (TSVQ) and the multistage VQ (MSVQ)-when used over noisy ch annels are analyzed. An algorithm is developed for the design of chann el-matched TSVQ (CM-TSVQ) and channel-matched MSVQ (CM-MSVQ) under the squared-error criterion. Extensive numerical results are given for th e memoryless Gaussian source and the Gauss-Markov source with correlat ion coefficient 0.9. Comparisons with the ordinary TSVQ and MSVQ desig ned for the noiseless channel show substantial improvements when the c hannel is very noisy. The CM-MSVQ, which can be regarded as a block-st ructured combined source-channel coding scheme, is then compared with a block-structured tandem source-channel coding scheme (with the same block length as the CM-MSVQ). For the Gauss-Markov source, the CM-MSVQ outperforms the tandem scheme in all cases that the authors have cons idered. Furthermore, it is demonstrated that the CM-MSVQ is fairly rob ust to channel mismatch.