Optimal companding vector quantization for circularly symmetric sources

In this paper, it is shown that optimal Z_2 lattice vector quantization can be implemented using radial companding technique. We derive the optimal vector compressor function for radial compander of memoryless Gaussian source. This result is obtained by taking into consideration the source geometry and by establishing the relation between the volumes and the point densities at the compressor input and compressor output. We also derive the linearized model – the piecewise linear compander. Its performance closely approaches that of optimal vector quantization. For example, for R = 8 bits/dimension and L = 16 regions, the difference between corresponding distortions is about 0.037 dB, while the asymptotic performances are identical.