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Abstract-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 complexity. An asymptotic analysis of the tradeoff between gain quantization and shape quantization is also given.

A new class of spherical codes called wrapped spherical codes is constructed by "wrapping" any sphere packing 3 in Euclidean space onto a finite subset of the unit sphere in one higher dimension. The mapping preserves much of the structure of 3, and unlike previously proposed maps, the density of wrapped spherical codes approaches the density of 3 as the minimum distance approaches zero. We show that this implies that the asymptotically maximum spherical coding density is achieved by wrapped spherical codes whenever 3 is the densest possible sphere packing.

We compare the capacities of M-ary pulse position modulation (PPM) on Gaussian and Webb channels, which are often used to model optical channels with avalanche photodiode (APD) detectors. Both types of channels exhibit the same brickwall thresholds on minimum signal-to-noise ratio per information bit (bit-SNR) for different values of M .

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