A coding theorem for secret sharing communication systems with two Gaussian wiretap channels

A coding theorem is proved for the secret sharing communication system (SSCS) with two Gaussian wiretap channels. This communication system is an extension of both the SSCS with two noiseless channels and the Gaussian wiretap channel (GWC). The admissible region of rates and security levels for the SSCS with two GWCs is described by the capacities and secrecy capacities of two GWCs. The following three cases are considered: two wiretappers cannot cooperate with each other: they can cooperate to decipher the transmitted information; and it is not known whether they can cooperate or not.