Generalized upper bound of agreement probability for extracting common random bits from correlated sources

Suppose that both Alice and Bob receive independent random bits without any bias, which are influenced by an independent noise. From the received random bits, Alice and Bob are willing to extract common randomness, without any communication. The extracted common randomness can be used for authentication or secrets. Recently, Bogdanov and Mossel derived an upper bound of the agreement probability, based on the min-entropy of outputs. In this paper, we derive a generalized upper bound of the probability of extracting common random bits from correlated sources, using the Rènyi entropy of order 1/(1-ε), where e is the error probability of the binary symmetric noise. It is shown that the generalized upper bound is always less than or equal to the previous bound.