This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length resolvability. Previous study has derived the general formula of the $\epsilon$-variable-length resolvability. We derive the general formula of the $\epsilon$-variable-length intrinsic randomness. Namely, we characterize the supremum of the mean length under the constraint the value of the average variational distance is smaller than or equal to some constant. Our result clarifies a dual relationship between the general formula of $\epsilon$-variable-length resolvability and that of $\epsilon$-variable-length intrinsic randomness. We also derive a lower bound of the quantity characterizing our general formula.
翻译:本文考虑了可变长度内在随机性问题。 我们从与可变长度可溶性问题配方的双重关系的角度提出平均变化距离作为性能标准。 先前的研究得出了 $\ epsilon$- 可变长度可溶性的一般公式。 我们得出了 $\ exsilon$- 可变长度的内在随机性的一般公式。 也就是说, 我们确定受约束的平均长度的超值值值, 平均变化距离的值小于或等于某种恒定值。 我们的结果澄清了 $\ exsilon- 可变长度可溶性一般公式与 $\ epsilon- 可变长度可溶性内随机性一般公式之间的双重关系。 我们还得出了我们通用公式数量特点的较低界限。