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 1 onto a sphere in , 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

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... y. An asymptotic analysis of the tradeoff between gain quantization and shape quantization is also given. Index Terms-Data compression, Gaussian source, lattice coding, vector quantization.