  The effect of "good", point-to-point capacity achieving, code sequences on an
additional signal, of bounded variance, transmitted over the additive Gaussian
noise channel is examined. For such code sequences, it is shown that their
effect, in terms of mutual information, on the additional bounded variance
signal, is as if additional additive Gaussian noise has been transmitted.
Moreover, the analysis shows that for reliable communication the bounded
variance signal must be completely estimated by the receiver (i.e., the minimum
mean-square error tends to zero). This result resolves the "Costa Conjecture"
regarding the corner points of the two-user Gaussian interference channel for
code sequences of bounded variance, and shows that both messages must be
reliably decoded.
