Uniform Distribution on $(n-1)$-Sphere: Rate-Distortion under Squared Error Distortion
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909066135076864 |
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| author | Dytso, Alex Cardone, Martina |
| author_facet | Dytso, Alex Cardone, Martina |
| contents | 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, $n \to \infty$). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04248 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform Distribution on $(n-1)$-Sphere: Rate-Distortion under Squared Error Distortion Dytso, Alex Cardone, Martina Information Theory 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, $n \to \infty$). |
| title | Uniform Distribution on $(n-1)$-Sphere: Rate-Distortion under Squared Error Distortion |
| topic | Information Theory |
| url | https://arxiv.org/abs/2401.04248 |