On logarithmic spherical vector quantization

Logarithmic spherical vector quantization (LSVQ) is a specific type of gain-shape vector quantization (VQ), where input vectors are decomposed into a gain and a shape component which are quantized independently. In this contribution, novel theoretical results on LSVQ are presented: It will be shown that, for high bit rates, with logarithmic (A-Law) scalar quantization (SQ) of the gain and spherical vector quantization (SVQ) of the shape component a signal-to-noise ratio (SNR) is achieved which is approximately independent of the input source distribution. In addition, a detailed theoretical analysis leads to a lower bound for the quantization distortion related to SVQ. By introducing approximations for the assumption of high bit rates, this bound is the basis for the computation of the optimal allocation of bit rate to the gain and the shape quantizer, respectively, and yields an estimate for the achievable SNR for LSVQ.