CTH14-5: Probability Density Functions of Logarithmic Likelihood Ratios in Phase Shift Keying BICM

Bit-interleaved coded modulation (BICM) is a coded-modulation scheme where 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 closed-form expressions for PDF of reliability metrics in BICM based on M-PSK with gray mapping. Such probabilistic description of BICM channel is necessary to calculate the channel´s information-theoretic parameters such as capacity, or cut-off rate but it is also a tool required to analyze the performance of coded transmission.