Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: A Combinatorial Approach to Evaluation of Reliability of the Receiver Output for BPSK Modulation with Spatial Diversity. | A Combinatorial Approach to Evaluation of Reliability of the Receiver Output for BPSK Modulation with Spatial Diversity S. Bliudze D. Krob bliudze dk @ LIX Ecole Polytechnique Route de Saclay 91128 Palaiseau Cedex France Submitted Jul 22 2004 Accepted Jan 3 2006 Published Jan 7 2006 Mathematics Subject Classifications 05E05 05E10 Abstract In the context of soft demodulation of a digital signal modulated with Binary Phase Shift Keying BPSK technique and in presence of spatial diversity we show how the theory of symmetric functions can be used to compute the probability that the log-likelihood of a recieved bit is less than a given threshold e. We show how such computation can be reduced to computing the probability that U V e denoted P U V e where U and V are two real random variables such that U XN 1 IT. - and V XN 1 vi 2 where the Ui s and Vi s are independent centered complex Gaussian variables with variances E ui 2 Xi and E vi 2 8i. We give two expressions in terms of symmetric functions over the alphabets A ố1 . ỎN and X x1 . ỵN for the first 2N 1 coefficients of the Taylor expansion of P U V e in terms of e. The first one is a quotient of multiSchur functions involving two alphabets derived from alphabets A and X which allows us to give an efficient algorithm for the computation of these coefficients. The second expression involves a certain sum of pairs of Schur functions S A and s X where A and j are complementary shapes inside a N X N rectangle. We show that such a sum has a natural combinatorial interpretation in terms of what we call square tabloids with ribbons and that there is a natural extension of the Knuth correspondence that associates a 0 1 -matrix to each square tabloid with ribbon. We then show that we can completely characterise the 0 1 -matrices that arise from square tabloids with ribbons under this correspondence. THE ELECTRONIC JOURNAL OF COMBINATORICS 13 2006 R2 1 1 Introduction In this paper we show how combinatorial .
