Probability Density Functions of L‐values

To characterize complex systems such as bit‐interleaved coded modulation (BICM) receivers, it is convenient to study their building blocks independently. An important building block in a BICM receiver is the demapper, whose role consists in calculating the L‐values. The chapter explains how to calculate the probability density functions (PDFs) for 1D and 2D constellations, respectively. It shows how to find the tessellation regions for arbitrary 2D constellations and labelings. The chapter discusses the PDFs of the L‐values in fading channels, and explains the first Gaussian model for the PDF of the L‐values, namely, the so‐called consistent model (CoM). It also provides a model for the PDF of the L‐values, such that (i) its parameters are easy to find, (ii) its form simplifies operations on the PDF of the L‐values, and (iii) the integration over its tail accurately estimates the actual value of the probability of error.