Optimal sequential scalar quantization of vectors

Balasubramanian et al. (1993) proposed an efficient vector quantization method called sequential scalar quantization (SSQ). In this method, the scalar components of the vector are individually quantized in a sequence, with the quantization of each component utilizing conditional information from the quantization of previous components. It has been shown that SSQ performs far better than conventional independent scalar quantization, while offering significant computational advantage over conventional VQ techniques. However, the design technique was a greedy method. The present authors use asymptotic quantization theory to derive a globally optimal design procedure for SSQ. With this method, the quantization of a scalar depends not only on its marginal density conditioned on the previously quantized scalars, but also on the distribution of the unquantized scalars. They also present simulation results to illustrate the relative performance of these two design methods with a moderate number of quantization levels