Consider a noisy signal which transmits an unknown bit and a known reference bit. The receiver takes \(N\) measurements of the signal. The authors use symmetric functions to compute the Taylor series for the probability that the log-likelihood ratio for correct demodulation is less than some bound \(\epsilon\); that is, that the receiver is either wrong or not confidently that the bit was decoded properly, and could make an error in soft-decision decoding. A combinatorial interpretation for the constant term, which corresponds to the hard-decision probability, was given by D. Krob and E. A. Vassilieva [Discrete Appl. Math. 145, 403–421 (2005; Zbl 1061.68117)]. The first \(2N-1\) terms of the Taylor series can be computed from a quotient of multi-Schur functions in two alphabets, which leads to an efficient algorithm for their computation. They can also be written as a sum of products of certain pairs of Schur functions \(s_\lambda(\Delta)s_\mu(X)\) where the tableaux \(\lambda\) and the transpose of \(\mu\) are complementary shapes inside the \(N\times N\) square. The sum has a natural combinatorial interpretation in terms of pairs of tableaux which fit inside the square with a “ribbon” between them. There is a natural extension of the Robinson-Schensted-Knuth correspondence which associates a \((0,1)\)-matrix to each such “square tabloid with ribbon.”