The Effect of Maximal Rate Codes on the Interfering Message Rate

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.