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I haven't dug deeper, but the claim that the von Neumann approach is optimal does not seem intuitively correct. It seems like you could squeeze a tiny bit more entropy from it -- basically, if you reject two pairs in a row, the nature of that rejection tells you something.

    HT xx -> H
    TH xx -> T
    HH TT -> H
    TT HH -> T


You're correct. There are more sophisticated extractors like Elias' and Peres' that do better, asymptotically achieving the upper bound given infinite data.

See https://peteroupc.github.io/randextract.html


OP here.

Thanks for that, that's obviously better in terms of bitrate, I haven't thought of that. Any two bit sequences with equal probability can be used to emit either a 0 and 1..




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