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Non-achievability of mutual information for the XOR source
XOR non-achievability conjecture. For some, or equivalently in the paper's general formulation for a general distribution $P_{X,Y}$ , the rate $I(X;Y)$ is not achievable:
Conjectureopeninformation-theory secret-key-agreement source-model-codingarXiv posted 2 days ago

Non-achievability of mutual information for the XOR source