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 R
₁
and the rate of each subcode R
₂
. Two different representations are given for this function and its basic properties are provided. We also characterize the region of pairs of rates (R
₁
, R
₂
) 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.