Gosset Low Complexity Vector Quantization with Application to Audio Coding

Abstract:
This paper introduces a novel and highly efficient realization of a spherical vector quantizer (SVQ), the "Gosset Low Complexity Vector Quantizer" (GLCVQ). The GLCVQ codebook is composed of vectors that are located on spherical shells of the eightdimensional Gosset lattice E8. A high encoding efficiency is achieved by representing the spherical vector codebook as aggregated permutation codes. Compared to previous algorithms, the computational complexity and memory consumption is further reduced by grouping the so-called classleader vectors into a significantly lower number of classleader root vectors based on separate handling of signs and magnitudes for each vector coordinate. The GLCVQ concept can be generalized to vector dimensions that are multiples of eight. In particular, GLCVQ for 16-dimensional vectors is used in Amd. 6 to ITU-T Rec. G.729.1 for super-wideband speech and audio coding.