A unified approach to tree-structured and multistage vector quantization for noisy channels

The large encoding complexity and sensitivity to channel errors of vector quantization (VQ) are discussed. The performance of two low-complexity VQs-the tree-structured VQ (TSVQ) and the multistage VQ (MSVQ)-when used over noisy channels are analyzed. An algorithm is developed for the design of channel-matched TSVQ (CM-TSVQ) and channel-matched MSVQ (CM-MSVQ) under the squared-error criterion. Extensive numerical results are given for the correlation coefficient 0.9. Comparisons with the ordinary TSVQ and MSVQ designed for the noiseless channel show substantial improvements when the channel is very noisy. The CM-MSVQ, which can be regarded as a block-structured combined source-channel coding scheme, is 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 considered. It is demonstrated that the CM-MSVQ is fairly robust to channel mismatch