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Since δ can be chosen arbitrarily small, R can be chosen to be as close to H (Y : X) as desired. Now getting the maximum over the prior probabilities of the strings Shannon’s result is found. Shannon’s noisy channel coding theorem: For a noisy channel N the capacity is given by C (N ) = max H (Y : X) , p(x) where the maximum is taken over all input distributions p (x) (a priori distributions) for X, for one use of the channel, and Y is the corresponding induced random variable at the output of the channel.
Smolin. Experimental Quantum Cryptography. J. Cryptology, 5: 3-28 (1992).  D. S. Bethune and W. P. Risk. An autocompensating quantum key distribution system using polarization splitting of light. In IQEC’98 Digest of Postdeadline Papers, pages QPD12-2, Optical Society of America, Washington, DC (1998).  Donald S. Bethune and William P. Risk. An autocompensating fiber-optic quantum cryptography system based on polarization splitting of light. J. Quantum Electronics, 36(3): 100 (2000).  A.