Exact Correct-Decoding Exponent of the Wiretap Channel Decoder

The performance of the achievability scheme for Wyner´s wiretap channel model is examined from the perspective of the probability of correct decoding, P_c, at the wiretap channel decoder. In particular, for finite-alphabet memoryless channels, the exact random coding exponent of P_c is derived as a function of the total coding rate R₁ and the rate of each subcode R₂. Two different representations are given for this function and its basic properties are provided. We also characterize the region of pairs of rates (R₁, R₂) of full security in the sense of the random coding exponent of P_c, in other words, the region where the exponent of this achievability scheme is the same as that of blind guessing at the eavesdropper side. Finally, an analogous derivation of the correct-decoding exponent is outlined for the case of the Gaussian channel.