Scalable coding rate-distortion bounds, and conditions for their coincidence with non-scalable rate-distortion bounds, were derived by W.H.R. Equitz and T.M. Cover (1991) and B. Rimoldi (1994). However, there has always been an implicit assumption of a tree structured vector quantization (TSVQ) scheme, which requires extensive memory usage. On the other hand, in most practical applications, additive structures such as multi-stage vector quantization (MSVQ) are preferred. In this paper, we analyze the bounds for MSVQ.
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