Logarithmic Cubic Vector Quantization: Concept and analysis

In this paper, we analyze Logarithmic Cubic Vector Quantization (LCVQ), a novel type of gain-shape vector quantization (GSVQ). In LCVQ, the vector to be quantized is decomposed into a gain factor and a shape vector which is a normalized version of the input vector. Both components are quantized independently and transmitted to the decoder. Compared to other GSVQ approaches, in LCVQ the input vectors are normalized based on the maximum norm (also denoted as L
_∞
-norm) instead of the typically used Euclidean norm (L
₂
-norm). Therefore, all shape vectors are located on the surface of the unit hypercube. As a conclusion, the shape vector quantizer can be realized based on uniform scalar quantizers yielding low computational complexity as well as high memory efficiency even in case of very high vector dimensions. In this paper, the concept of LCVQ is presented. Also, theoretical quantization performance measures for LCVQ as well as the optimal allocation of bit rate for gain factor and shape vector are derived. In order to assess the proposed LCVQ approach, the quantization performance achieved by LCVQ is compared to results which were recently derived for Logarithmic Spherical Vector Quantization (LSVQ), another highly efficient GSVQ scheme proposed in.