Uniform Distribution on $(n-1)$-Sphere: Rate-Distortion under Squared Error Distortion

Alex Dytso; Martina Cardone

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arXiv · 2401.04248

Uniform Distribution on $(n-1)$-Sphere: Rate-Distortion under Squared Error Distortion

Alex Dytso·Martina Cardone

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Abstract

This paper investigates the rate-distortion function, under a squared error distortion $D$, for an $n$-dimensional random vector uniformly distributed on an $(n-1)$-sphere of radius $R$. First, an expression for the rate-distortion function is derived for any values of $n$, $D$, and $R$. Second, two types of asymptotics with respect to the rate-distortion function of a Gaussian source are characterized. More specifically, these asymptotics concern the low-distortion regime (that is, $D \to 0$) and the high-dimensional regime (that is, $n \to \infty$).

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Alex Dytso, Martina Cardone. 2024-01-08. Uniform Distribution on $(n-1)$-Sphere: Rate-Distortion under Squared Error Distortion. https://arxiv.org/abs/2401.04248

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