We consider a standard two-source model for uniform common randomness (UCR) generation, in which Alice and Bob observe independent and identically distributed (i.i.d.) samples of a correlated finite source and where Alice is allowed to send information to Bob over an arbitrary single-user channel. We study the \(\boldsymbol{\epsilon}\)-UCR capacity for the proposed model, defined as the maximum common randomness rate one can achieve such that the probability that Alice and Bob do not agree on a common uniform or nearly uniform random variable does not exceed \(\boldsymbol{\epsilon}.\) We establish a lower and an upper bound on the \(\boldsymbol{\epsilon}\)-UCR capacity using the bounds on the \(\boldsymbol{\epsilon}\)-transmission capacity proved by Verd\'u and Han for arbitrary point-to-point channels.

翻译：我们考虑一种用于均匀公共随机数生成的经典双信源模型，其中Alice和Bob观测到相关有限信源的独立同分布样本，且Alice可通过任意单用户信道向Bob发送信息。我们研究该模型下的\(\boldsymbol{\epsilon}\)-均匀公共随机数容量，定义为可达到的最大公共随机数速率，使得Alice和Bob未能就公共均匀或近似均匀随机变量达成一致的概率不超过\(\boldsymbol{\epsilon}\)。利用Verdú和Han针对任意点对点信道证明的\(\boldsymbol{\epsilon}\)-传输容量的界，我们建立了该\(\boldsymbol{\epsilon}\)-均匀公共随机数容量的下界与上界。