Phase Transitions of the Additive Uniform Noise Channel with Peak Amplitude and Cost Constraint
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915553877164032 |
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| author | Stapmanns, Jonas Dias, Catarina Eilers, Luke Kühn, Tobias Pfister, Jean-Pascal |
| author_facet | Stapmanns, Jonas Dias, Catarina Eilers, Luke Kühn, Tobias Pfister, Jean-Pascal |
| contents | Under which condition is quantization optimal? We address this question in the context of the additive uniform noise channel under peak amplitude and cost constraints. We compute analytically the capacity-achieving input distribution as a function of the noise level, the average cost constraint, and the curvature of the cost function. We find that when the cost function is concave, the capacity-achieving input distribution is discrete, whereas when the cost function is convex and the cost constraint is active, the support of the capacity-achieving input distribution spans the entire interval. For the cases of a discrete capacity-achieving input distribution, we derive the analytical expressions for the capacity of the channel. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_12427 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Phase Transitions of the Additive Uniform Noise Channel with Peak Amplitude and Cost Constraint Stapmanns, Jonas Dias, Catarina Eilers, Luke Kühn, Tobias Pfister, Jean-Pascal Information Theory 94A15, 94A40 Under which condition is quantization optimal? We address this question in the context of the additive uniform noise channel under peak amplitude and cost constraints. We compute analytically the capacity-achieving input distribution as a function of the noise level, the average cost constraint, and the curvature of the cost function. We find that when the cost function is concave, the capacity-achieving input distribution is discrete, whereas when the cost function is convex and the cost constraint is active, the support of the capacity-achieving input distribution spans the entire interval. For the cases of a discrete capacity-achieving input distribution, we derive the analytical expressions for the capacity of the channel. |
| title | Phase Transitions of the Additive Uniform Noise Channel with Peak Amplitude and Cost Constraint |
| topic | Information Theory 94A15, 94A40 |
| url | https://arxiv.org/abs/2510.12427 |