We investigate the problem of common randomness (CR) generation in the basic two-party communication setting in which a sender and a receiver aim to agree on a common random variable with high probability. The terminals observe independent and identically distributed (i.i.d.) samples of sources with an arbitrary distribution defined on a Polish alphabet and are allowed to communicate as little as possible over a noisy, memoryless channel. We establish single-letter upper and lower bounds on the CR capacity for the specified model. The derived bounds hold with equality except for at most countably many points where discontinuity issues might arise.

翻译：我们研究了在基本两方通信场景中的公共随机性生成问题，其中发送方和接收方旨在以高概率就公共随机变量达成一致。终端观测到定义在波兰字母表上具有任意分布的独立同分布源样本，并允许通过无噪声无记忆信道进行尽可能少的通信。我们为该指定模型建立了公共随机性容量的单字母上界和下界。推导的界在除最多可数个可能产生不连续性的点之外均以等式成立。