Transform coding with backward adaptive updates
IEEE Transactions on Information Theory
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Designing a lossy source code remains one of the important topics in information theory, and has a lot of applications. Although plain vector quantization (VQ) can realize any fixed-length lossy source coding, it has a serious drawback in the computation cost. Companding vector quantization (CVQ) reduces the complexity by replacing vector quantization with a set of scalar quantizations. It can represent a wide class of practical VQs, while the structure in CVQ restricts it from representing every lossy source coding. In this article, we propose an optimization method for parametrized CVQ by utilizing a newly derived distortion formula. To test its validity, we applied the method especially to transform coding. We found that our trained CVQ outperforms Karhunen-Loëve transformation (KLT)-based coding not only in the case of linear mixtures of uniform sources, but also in the case of low bit-rate coding of a Gaussian source.