CTH14-3: Probability Density Function of Reliability Metrics in BICM with Arbitrary Modulation: Closed-form through Algorithmic Approach

In the popular bit-interleaved coded modulation (BICM) the output of the channel encoder and the input of the modulator are separated by a bit-level interleaver. From the decoder´s point of view, the modulator, the transmission channel, and the demodulator (calculating bits´ reliability metrics) become a memoryless BICM channel with binary inputs and real outputs. The BICM channel´s outputs (reliability metrics) are known to be Gaussian for binary- or quaternary phase shift keying but no expression for their probability density function (PDF) is known for higher-order modulation. We fill this gap presenting an algorithmic method to calculate closed-form expressions for the PDF of reliability metrics in BICM with arbitrary modulation and bits-to-symbol mapping. Such probabilistic description of BICM channel provides a useful tool to analyze, from an information- theoretic point of view, any BICM constellation/mapping design.