Use of Gaussian codebooks for residual vector quantizers

A well known result of rate-distortion theory states that, under broad conditions, the quantization error has a Gaussian distribution. It is also known that a Gaussian memoryless source is successively refinable. These results indicate that the use of code books designed for a generic Gaussian source for different stages of a residual vector quantizer does not result in loss of performance. In this work, we present a residual vector quantizer using an optimal (LBG) vector quantizer in the first stage and a Gaussian codebook in the other stages. The closeness of the distribution of the error signals to the Gaussian distribution is examined and it is shown that while the rate-distortion theoretic results are true only when the rate of the first stage is very high, in practice, even at moderate rates, the loss in the optimality is quite small.