Gaussian source coding with spherical codes

Abstract

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.

On concentric spherical codes and permutation codes with multiple initial codewords

“…Sakrison [2] first analyzed the performance of spherical codes for memoryless Gaussian sources. Following [1], [2], the distortion can be decomposed as…”

“…Then we address a portion of the integer partition design problem which is the sizing of the subcodebooks. For this, we extend the high-resolution analysis of [1].…”

“…V returns to the general case, with integer partitions that are not necessarily equal. We develop fixed-and variable-rate generalizations of the wrapped spherical gain-shape vector quantization of Hamkins and Zeger [1] for the purpose of guiding the rate allocation problem. These results may be of independent interest.…”

Multiproduct Uniform Polar Quantizer

“…In [3], [4] unrestricted polar quantizers were analyzed, using the optimal companding function for the quantization of the magnitude r. In [5], [6] the product uniform polar quantization was considered. The product polar quantizer with the companding function optimal for scalar but not for polar quantization, was considered in [7]. Embedded product and unrestricted polar quantizers were considered in [8].…”

“…The asymptotic analysis is usually used for the designing of polar quantizers [3][4][5][6][7][8][9][10][11][12][13][14]. Hence, the asymptotic analysis will be applied in this paper.…”