Sequential Scalar Quantization Of Vectors: An Analysis

We propose an efficient vector quantization (VQ) technique which we call sequential scalar quantization (SSQ). 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. Unlike conventional independent scalar quantization (ISQ), SSQ has the ability to exploit inter-data correlation. At the same time, since quantization is performed on scalar rather than vector variables, SSQ offers a significant computational advantage over conventional VQ techniques, and is easily amenable to a hardware implementation. In order to analyze the performance of SSQ, we appeal to asymptotic quantization theory where the codebook size is assumed to be large. Closed form expressions are derived for the quantizer mean squared error (MSE). These expressions are used to compare the asymptotic performance of SSQ with other VQ techniques. We also demonstrate the use of asympto..