Round-Preserving Asymptotic Compression of Prior-Free Interactive Protocols

Gurleen Padda; Dave Touchette

doi:10.1109/itw62417.2025.11240394

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arXiv · 2507.13464

Round-Preserving Asymptotic Compression of Prior-Free Interactive Protocols

Gurleen Padda·Dave Touchette

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Abstract

There is a close relationship between the communication complexity and information complexity of communication problems, as demonstrated by results such as Shannon's noiseless source coding theorem, and the Slepian-Wolf theorem. Here, we study this relationship in the prior-free and interactive setting, where we provide an alternate proof for the result of Braverman [SIAM Review, vol. 59, no. 4, 2017], that the amortized communication complexity of simulating a prior-free interactive communication protocol, is equal to its prior-free information cost. While this is a known result, our approach addresses the need for a more natural proof of it. We also improve on the result by achieving round preservation, and using a bounded quantity of shared randomness. We do this by showing that the communicating parties can produce a reliable estimate of the joint type, or empirical distribution, of their inputs. This estimate is then used in our protocol for the prior-free reverse Shannon theorem with side information at the receiver. These results are then generalized to the interactive setting to obtain our main result.

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Gurleen Padda, Dave Touchette. 2025-07-17. Round-Preserving Asymptotic Compression of Prior-Free Interactive Protocols. https://doi.org/10.1109/itw62417.2025.11240394

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