On the capacity loss due to separation of detection and decoding

The performance loss due to separation of detection and decoding on the binary-input additive white Gaussian noise (AWGN) channel is quantified in terms of mutual information. Results are reported for both the code-division multiple-access (CDMA) channel in the large system limit and the intersymbol interference (ISI) channel. The results for CDMA rely on the replica method developed in statistical mechanics. It is shown that a previous result of Shamai and Verdu found for Gaussian input alphabet holds also for binary input alphabets. For the ISI channel, the performance loss is calculated via the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. Comparisons are made to the capacity of separate detection and decoding using suboptimum detectors such as a decision-feedback equalizer.