Coding theorem for secret sharing communication systems with two noisy channels

The coding theorem is proved for the secret sharing communication system (SSCS) with two noisy channels, each of which is a broadcast channel characterized by P( y,z, Ix,), j = 1,2; it is assumed that the legitimate channel ( Xj + Y,) is less noisy than the wiretapped channel ( Xj --f Z,), The code (f, +) for the SSCS is defined by two mappings: (Xp,Xp)=f(SK,T) and s^=q5(Yp,YaNz) where 7’ is an arbitrarily chosen random number and S is an independent identically distributed source output that must be transmitted to the legitimate receiver with an arbitrarily small error. The rate of each channel is given by N,/K while the security level for each wiretapper can be evaluated by (l/K)H(.SKIZ,~). The admissible region of rates and security levels is given by a “single-letter characterization.” BCC 1 S” t Source Encoder Decoder S-f @ es Legitimate BCC2 4 Receiver VP ZP Wi retapper2 Fig. 1. SSCS with two noisy channels.