论文标题
从具有可数字母的来源的常见随机性产生
Common Randomness Generation from Sources with Countable Alphabet
论文作者
论文摘要
我们研究了一个标准的两源模型，用于共同的随机性（CR）产生，其中爱丽丝和鲍勃通过观察独立和相同分布的（i.i.d.）样本的相关源中相关源的无限无限字母字母的样本来产生一个共同的随机变量，具有很高的一致性。还允许两方在嘈杂的无内存频道上尽可能少地进行交流。在我们的工作中，我们为提出的模型提供了一个单行的公式，并为其提供了严格的证明。这是一个具有挑战性的场景，因为某些有限的字母特性，即熵的特性不能扩展到无数的无限情况。值得注意的是，众所周知，香农熵实际上在所有概率分布中都是不合时宜的，并具有无限的支持。
We study a standard two-source model for common randomness (CR) generation in which Alice and Bob generate a common random variable with high probability of agreement by observing independent and identically distributed (i.i.d.) samples of correlated sources on countably infinite alphabets. The two parties are additionally allowed to communicate as little as possible over a noisy memoryless channel. In our work, we give a single-letter formula for the CR capacity for the proposed model and provide a rigorous proof of it. This is a challenging scenario because some of the finite alphabet properties, namely of the entropy can not be extended to the countably infinite case. Notably, it is known that the Shannon entropy is in fact discontinuous at all probability distributions with countably infinite support.
