Extraction of optimally unbiased bits from a biased source

We explore the problem of transforming n independent and identically biased {-1,1}-valued random variables, X₁, ..., X _n, into a single {-1,1} value, f(X₁, ..., X_n ), so that this result is as unbiased as possible. In general, no function f produces a completely unbiased result. We perform the first study of the relationship between the bias b of these X_i and the rate at which f(X₁, ..., X_n) can converge to an unbiased {-1,1} random variable (as n→∞)