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This universal decoder is shown to be closely related to the Lagrange-optimized decoder of Oosterwijk et al. and the empirical mutual information decoder of Moulin.
In between, Section 3.4 discusses a completely different approach to obtain a universal simple decoder (based on the empirical mutual information decoder of Moulin [25]) and shows how in the end the result is again quite similar.
We also showed how the proposed universal decoder is very similar to both Oosterwijk et al.'s decoder h and an approximation of Moulin's empirical mutual information decoder m for 0≪p≪1 by begin{array}{*{20}l} c cdot g x,y,p) sim h x,y,p) sim n cdot m x,y,p), end{array}.
To construct this decoder, we start with the empirical mutual information decoder previously proposed by Moulin [25], and for now, let us assume p i ≡p is fixed.4 With this decoder, a user is assigned a score of the form begin{array}{*{20}l} S_{j} &= sum_{x,y} hat{f}_{X,Y|P} x,y|p) lnleft(frac{hat{f}_{X,Y|P} x,y|p)}{hat{f}_{X|P}(x|p)hat{f}_{Y|P} y|p)}right) end{array}.
For the interleaving attack strategy, the Bayesian approximation of the empirical mutual information decoder of (11) satisfies begin{array}{*{20}l} m x,y,p) = left{begin{array}{cc} lnleft(1 + frac{p}{n(1 - p)}right) & text{if}~ x = y = 0; !!!!!!!!!!!!!lnleft(1 - frac{1}{n}right) & !!!!!!!!!!!!text{if}~ x neq y; !!!!!!lnleft(1 + frac{1 - p}{np}right) & text{if}~ x = y = 1.
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Assuming an MMSE decoder, the mutual information between the k th transmitter and its intended receiver k can be expressed as [11] R k ( w ) = log 2 I N + p ∑ j H kj W V j V j H W H H kj H I N + p ∑ j ≠ k H kj W V j V j H W H H kj H, (9).
In the cases of MMSE-IC and MMSE-IC1 (Figure 6c and Figure 6d, respectively), the characteristics present a lower mutual information than the LC-K-Best decoder when I A1<0.85.
Given a code, the EXIT function associated is defined by the relation between the a priori mutual information at the input of the decoder (commonly denoted as I a ) and the corresponding extrinsic mutual information I e at its output, i.e., I e =T(I a ).
In this case, Corollary 1 of [20] shows that G i, OPT is the optimum decoder and the mutual information I Ei in (8) becomes I Ei = log 2 σ s j 2 C ij F j F j * C ij * + Φ n i Φ n i, i, j = 1, 2 and i ≠ j. (10).
Compute the extrinsic information from the channel decoder, i.e., mutual information I E or (text {MMSE}_{text {ext}}^{B}) based on the PDF of L E (L A (y π,t,S π,t ),y ′(t)),e ′(t)).
LC-K-Best decoder has slightly less mutual information than STS-SD.
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