Replica Analysis of Performance Loss Due to Separation of Detection and Decoding in CDMA Channels

Theoretically, maximum information transmission in a CDMA channel is achieved when the receiver performs joint user detection and decoding. Performance will be reduced if the receiver performs user detection, followed by per-user decoding. We discuss, on the basis of the replica analysis, the loss in information-transmission capability of a CDMA channel, due to the separation of user detection and decoding. We generalize the analysis on a CDMA channel with additive Gaussian channel noise, by Guo and Verdu, IEEE Trans. Info. Theory, 2005, in such a way as to allow channel noise to be non-Gaussian and/or non-additive. The loss, in spectral efficiency, is shown to be represented in terms of conditional entropies of channel outputs, as well as mean-squared error of the posterior-mean estimator of channel inputs