On entropy-constrained Gaussian channel capacity via the moment problem
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908341867905024 |
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| author | Girish, Adway Shamai, Shlomo Telatar, Emre |
| author_facet | Girish, Adway Shamai, Shlomo Telatar, Emre |
| contents | We study the capacity of the power-constrained additive Gaussian channel with an entropy constraint at the input. In particular, we characterize this capacity in the low signal-to-noise ratio regime at small entropy. This follows as a corollary of the following general result on a moment matching problem: We show that for any continuous random variable with finite moments, the largest number of initial moments that can be matched by a discrete random variable of sufficiently small but positive entropy is three. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13814 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On entropy-constrained Gaussian channel capacity via the moment problem Girish, Adway Shamai, Shlomo Telatar, Emre Information Theory Probability We study the capacity of the power-constrained additive Gaussian channel with an entropy constraint at the input. In particular, we characterize this capacity in the low signal-to-noise ratio regime at small entropy. This follows as a corollary of the following general result on a moment matching problem: We show that for any continuous random variable with finite moments, the largest number of initial moments that can be matched by a discrete random variable of sufficiently small but positive entropy is three. |
| title | On entropy-constrained Gaussian channel capacity via the moment problem |
| topic | Information Theory Probability |
| url | https://arxiv.org/abs/2501.13814 |