On the generalized mutual information of BICM systems with approximate demodulation

We consider a generic bit-interleaved coded modulation (BICM) systems with an approximate demodulator or log-likelihood ratio (LLR) computer. The performance of a BICM system with optimal demodulation has previously been characterized by Caire et al. in terms of the capacity of an independent parallel-channel model with binary inputs and (continuous) LLRs as outputs, and by Martinez et al. in terms of the generalized mutual information (GMI) where the BICM decoder is viewed as a mismatched decoder. Whereas GMI and capacity of the parallel-channel model coincide under optimal demodulation, they differ in general for the case of an approximate demodulator. Herein we show (i) that augmenting approximate BICM demodulators with scalar LLR correction increases the GMI and (ii) that the GMI of the LLR-corrected system coincides with the capacity of the parallel-channel model with binary inputs and outputs given by the approximate LLRs.