A new approach to calculating the exact transition probability and bit error probability of arbitrary two-dimensional signaling

A general method is presented for the computation of the exact bit error probability for arbitrary two-dimensional (2D) signaling with polygonal decision regions in various channel environments. This new approach is general in the sense that it applies to any coherent 2D constellation, any bit-to-symbol mapping, and various environments such as additive white Gaussian noise (AWGN) channels and slow fading channels with and without diversity reception and channel estimation error. The considered performance measures include the exact bit error probability, the symbol error probability, the mutual information and the error probabilities of individual bits in a constellation. The proposed new approach is exact and easy to evaluate, thus avoiding the need for computer simulation.