On the Smooth Renyi Entropy and Variable-Length Source Coding Allowing Errors

TL;DR

This paper investigates variable-length source coding with errors, demonstrating that smooth Renyi entropy characterizes the optimal exponential moment of codeword length in both non-asymptotic and asymptotic regimes.

Contribution

It establishes the role of smooth Renyi entropy in characterizing the exponential moment of codeword length for source coding with errors.

Findings

Smooth Renyi entropy characterizes optimal exponential moments

Results apply to both non-asymptotic and asymptotic regimes

Provides theoretical bounds for source coding with errors

Abstract

In this paper, we consider the problem of variable-length source coding allowing errors. The exponential moment of the codeword length is analyzed in the non-asymptotic regime and in the asymptotic regime. Our results show that the smooth Renyi entropy characterizes the optimal exponential moment of the codeword length.