Performance analysis of demodulation with diversity - A combinatorial approach I : Symmetric function theoretical methods

Dornstetter, Jean-Louis; Krob, Daniel; Thibon, Jean‐Yves; Vassilieva, Ekaterina A.

doi:10.46298/dmtcs.295

Discrete Mathematics &Amp; Theoretical Computer Science

2002

DOI: 10.46298/dmtcs.295

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Performance analysis of demodulation with diversity - A combinatorial approach I : Symmetric function theoretical methods

Jean-Louis Dornstetter¹,

Daniel Krob²,

Jean‐Yves Thibon³

et al.

Abstract: We present symmetric function theoretical methods for solving a performance analysis problem related with modulation protocols with diversity.

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Cited by 4 publications

References 7 publications

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Performance evaluation of demodulation with diversity—a combinatorial approach II: bijective methods

Krob

Vassilieva

2005

Discrete Applied Mathematics

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This paper is devoted to the presentation of a combinatorial approach for analyzing the performance of a generic family of demodulation methods used in mobile telecommunications. We show that a fundamental formula in this context is in fact highly connected with a slight modification of a very classical bijection of Knuth between pairs of Young tableaux of conjugate shapes and {0, 1}-matrices. These considerations allowed us to obtain the first explicit expressions for several important specializations of the performance evaluation formula that we studied.

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Performance evaluation of demodulation with diversity—a combinatorial approach II: bijective methods

Krob

Vassilieva

2005

Discrete Applied Mathematics

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The expansion of immaculate functions in the ribbon basis

Campbell

2017

Discrete Mathematics

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

Bliudze¹,

Krob²

2006

Electron. J. Combin.

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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 $\varepsilon$. We show how such computation can be reduced to computing the probability that $U-V < \varepsilon$ (denoted $P(U-V < \varepsilon)$) where $U$ and $V$ are two real random variables such that $U=\sum_{i=1}^N |u_i|^2$ and $V=\sum_{i=1}^N |v_i|^2$ where the $u_i$'s and $v_i$'s are independent centered complex Gaussian variables with variances ${\Bbb E}[\,|u_i|^2\,]=\chi_i$ and ${\Bbb E}[\,|v_i|^2\,]=\delta_i$. We give two expressions in terms of symmetric functions over the alphabets $\Delta=(\delta_1,\dots,\delta_N)$ and $X=(\chi_1,\dots,\chi_N)$ for the first $2N-1$ coefficients of the Taylor expansion of $P(U-V < \varepsilon)$ in terms of $\varepsilon$. The first one is a quotient of multi-Schur functions involving two alphabets derived from alphabets $\Delta$ 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 $s_\lambda(\Delta)$ and $s_\mu(X)$ where $\lambda$ and $\mu$ are complementary shapes inside a $N\times N$ 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.

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Performance analysis of demodulation with diversity - A combinatorial approach I : Symmetric function theoretical methods

Abstract: We present symmetric function theoretical methods for solving a performance analysis problem related with modulation protocols with diversity.

Cited by 4 publications

References 7 publications

Performance evaluation of demodulation with diversity—a combinatorial approach II: bijective methods

Performance evaluation of demodulation with diversity—a combinatorial approach II: bijective methods

The expansion of immaculate functions in the ribbon basis

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

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