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, Pc, at the wiretap channel decoder. In particular, for finite-alphabet memoryless channels, the exact random coding exponent of Pc 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 Pc, 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.

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