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Exact Channel Simulation under Exponential Cost
Hill, Spencer; Alajaji, Fady; Linder, Tamás
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https://hdl.handle.net/2142/130271
Description
- Title
- Exact Channel Simulation under Exponential Cost
- Author(s)
- Hill, Spencer
- Alajaji, Fady
- Linder, Tamás
- Issue Date
- 2025-09-17
- Keyword(s)
- Channel simulation
- Rényi entropy
- Rényi divergence
- α-mutual information
- Poisson functional representation
- Common randomness
- Variable-length codes
- Exponential cost
- Abstract
- In this work, we generalize results in exact channel simulation to an exponential communication cost, specifically to Campbell’s average codeword length L(t) of order t [1], and to Rényi’s entropy. In exact channel simulation, given a source of shared randomness, a sender wishes to communicate a message to the receiver so they can generate a sample from the conditional distribution PY |X. We lower bound the Campbell cost of channel simulation using any sampling algorithm, showing that it grows approximately as It+1(X; Y), where Iα is an appropriately defined α-mutual information of order α. Using the Poisson functional representation of Li and El Gamal [2], we prove an upper bound on L(t) whose leading α-mutual information term has order within ϵ of the lower bound. Our results reduce to the bounds of Harsha et al. [3] as t → 0. We also provide numerical examples for the additive white Gaussian noise channel, demonstrating that the upper and lower bounds are typically within 5-10 bits of each other.
- Publisher
- Allerton Conference on Communication, Control, and Computing
- Series/Report Name or Number
- 2025 61st Allerton Conference on Communication, Control, and Computing Proceedings
- ISSN
- 2836-4503
- Type of Resource
- Text
- Genre of Resource
- Conference Paper/Presentation
- Language
- eng
- Handle URL
- https://hdl.handle.net/2142/130271&&
- Copyright and License Information
- Copyright 2025 owned by the authors.
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61st Allerton Conference - 2025 PRIMARY
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