General BER Expression for One-Dimensional Constellations

A novel general ready-to-use Bit-Error Rate (BER) expression for one-dimensional constellations is developed. The BER analysis is performed for bit patterns that form a labeling. The number of patterns for equally spaced M-PAM constellations with different BER is analyzed. Current wireless communication systems are based on the Bit-Interleaved Coded Modulation (BICM) paradigm introduced in and later studied. One key element in these systems is the calculation of Logarithmic Likelihood Ratios (LLR, also known as L-values) for the received bits, which are passed to the channel decoder.