1 Probability Density Functions of Reliability Metrics for 16-QAM-Based BICM Transmission in Rayleigh Channel Leszek Szczecinski, Alex Alvarado, Rodolfo Feick § Institut National de la Recherche Scientifique, INRS-EMT, University of Qu´ ebec 800 de la Gaucheti` ere Ouest Suite 6900 Montr´ eal, H5A 1K6, Canada {leszek,alvarado}@emt.inrs.ca § Department of Electronics Engineering, Universidad T´ ecnica Federico Santa Mar´ ıa Avenida Espa˜ na 1680, Valpara´ ıso, Chile {feick}@elo.utfsm.cl Abstract In bit interleaved coded modulation (BICM), the probability density function (PDF) of the reli- ability metrics (L-values) fully defines the BICM transmission and may be used to analyze it from an information-theoretic point of view. In this paper, the closed-form expressions for the PDF of the L-values in Rayleigh fading channels for 16-QAM with Gray mapping are derived and contrasted with histograms of the L-values obtained via numerical simulations. The obtained closed-forms show that the PDF is either a sum of exponentials or is bounded by such a sum. Index Terms Logarithmic Likelihood Ratios, L-values, Quadrature Amplitude Modulation, Probability Density Function, Rayleigh Fading, LLR, 16-QAM, PDF. Research supported by NSERC, Canada (under research grant #249704-02), and by Conicyt, Chile (under research grant PBCT-ACT-11/2004). April 13, 2006 DRAFT