The Effect of Maximal Rate Codes on the Interfering Message Rate

TL;DR

This paper demonstrates that capacity-achieving codes in Gaussian channels cause interference equivalent to Gaussian noise, requiring complete decoding of interfering signals for reliable communication, thus resolving the Costa Conjecture.

Contribution

It proves that good codes induce Gaussian-like interference and that all messages must be decoded, resolving the Costa Conjecture for bounded variance codes.

Findings

Interference acts as Gaussian noise for capacity-achieving codes.

Reliable communication requires complete decoding of interfering signals.

The result confirms the necessity of decoding all messages in the interference channel.

Abstract

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.