Gaussian source coding with spherical codes

A fixed-rate shape-gain quantizer for the memoryless Gaussian source is proposed. The shape quantizer is constructed from wrapped spherical codes that map a sphere packing in ℝ^k-1 onto a sphere in ℝ^k, and the gain codebook is a globally optimal scalar quantizer. A wrapped Leech lattice shape quantizer is used to demonstrate a signal-to-quantization-noise ratio within 1 dB of the distortion-rate function for rates above 1 bit per sample, and an improvement over existing techniques of similar complexity. An asymptotic analysis of the tradeoff between gain quantization and shape quantization is also given