Soft Guessing Under Logarithmic Loss Allowing Errors and Variable-Length Source Coding

Shota Saito; Hamdi Joudeh

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arXiv · 2510.09015

Soft Guessing Under Logarithmic Loss Allowing Errors and Variable-Length Source Coding

Shota Saito·Hamdi Joudeh

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Abstract

This paper considers the problem of soft guessing under a logarithmic loss distortion measure while allowing errors. We find an optimal guessing strategy, and derive single-shot upper and lower bounds for the minimal guessing moments as well as an asymptotic expansion for i.i.d. sources. These results are extended to the case where side information is available to the guesser. Furthermore, a connection between soft guessing allowing errors and variable-length lossy source coding under logarithmic loss is demonstrated. The R\'enyi entropy, the smooth R\'enyi entropy, and their conditional versions play an important role.

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Shota Saito, Hamdi Joudeh. 2025-10-10. Soft Guessing Under Logarithmic Loss Allowing Errors and Variable-Length Source Coding. https://arxiv.org/abs/2510.09015

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