We say that the mutual information of a triple of binary strings a, b, c can be extracted if there exists a string d such that a, b, and c are independent given d, and d is simple conditional to each of the strings a, b, and c. It is proved that the mutual information between a, b, and c can be extracted if and only if the values of the conditional mutual informations I(a : b|c), I(a : c|b), and I(b : c|a) are negligible. The proof employs a non-Shannon-type information inequality (a generalization of the recently discovered Zhang–Yeung inequality).
Problems of Information Transmission – Springer Journals
Published: Oct 4, 2004
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