Geometric source coding and vector quantization

A geometric formulation is presented for source coding and vector quantizer design. Motivated by the asymptotic equipartition principle, the authors consider two broad classes of source codes and vector quantizers: elliptical codes and quantizers based on the Gaussian density function, and pyramid codes and quantizers based on the Laplacian density function. Elliptical and weighted pyramid vector quantizers are developed by selecting codewords as points in a lattice that lie on (or near) a specified ellipse or pyramid. The combination of geometric structure and lattice basis allows simple encoding and decoding algorithms.<>