Variable-length compression without prefix-free constraints and with side-information available at both encoder and decoder is considered. Instead of requiring the code to be error-free, we allow for it to have a non-vanishing error probability. We derive one-shot bounds on the optimal average codeword length by proposing two new information quantities; namely, the conditional and unconditional ε-cutoff entropies. Using these one-shot bounds, we obtain the second-order asymptotics of the problem under two different formalisms-the average and maximum probabilities of error over the realization of the side-information. While the first-order terms in the asymptotic expansions for both formalisms are identical, we find that the source dispersion under the average error formalism is, in most cases, strictly smaller than its maximum error counterpart. Applications to a certain class of guessing problems, previously studied by Kuzuoka (2020), are also discussed.

中文翻译：

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可变长度源色散在最大和平均误差准则下有所不同


考虑没有无前缀约束且具有编码器和解码器可用的辅助信息的可变长度压缩。我们不要求代码没有错误，而是允许它具有非消失的错误概率。我们通过提出两个新的信息量来导出最佳平均码字长度的一次性界限；即，条件和无条件 ε-截止熵。使用这些一次性界限，我们获得了两种不同形式下问题的二阶渐近性——实现辅助信息时的平均错误概率和最大错误概率。虽然两种形式主义的渐近展开中的一阶项是相同的，但我们发现平均误差形式主义下的源色散在大多数情况下严格小于其最大误差对应项。还讨论了 Kuzuoka (2020) 先前研究的某一类猜测问题的应用。