A Combinatorial Approach to Evaluation of Reliability of the Receiver Output for BPSK Modulation with Spatial Diversity

We consider log-likelihood of received bits for the classical approach to demodulation of digital signals modulated using Binary Phase Shift Keying (BPSK). Using the symmetric functions mechanism we obtain a stable and efficient algorithm allowing to compute the probability that this value is close to zero. Introducing a new class of combinatorial objects we provide a combinatorial interpretation of the formulae obtained with symmetric functions. Then we derive from the Robinson-Schensted-Knuth correspondence a bijection between this class and a subset of the set of {0, 1}-matrices. Finally we prove a theorem establishing the criteria that define this subset.