Integer metrics for binary input symmetric output memoryless channels

Consider a coded communication system where antipodal signaling is used over symmetric memoryless channels. A mismatch decoder employing metrics which assume values in a finite set of integers is used. Two performance measures for achievable rates are considered, the generalized cutoff rate and the mismatch capacity. Two different integer metric assignments which maximize these criteria are found. The optimal metric assignment holds for any binary input symmetric output memoryless channels. It is calculated explicitly for the faded additive white Gaussian noise channel with and without diversity, an interference channel model and the additive "Cauchy" channel. The difference in terms of achievable rates between decoding using the optimal continuous metric and integer metric is calculated for these channels. The degradation for fairly low number of quantization levels is found to be small, e.g. for nine quantization levels degradation is less than 0.3 dB for all analyzed channels. The sensitivity of the generalized cutoff rate and the mismatch capacity to the exact location of the quantization levels is rather mild. The difference between the mismatch capacity corresponding to the optimal integer quantization and the mismatch capacity obtained by the quantization which optimizes the generalized cutoff rate is found to be quite small.