Information Combining (Foundations and Trends in by Ingmar Land, Johannes Huber PDF

By Ingmar Land, Johannes Huber

ISBN-10: 1933019468

ISBN-13: 9781933019468

ISBN-10: 1933019980

ISBN-13: 9781933019987

Details Combining is an creation to the rules of data combining. the concept that is defined, the boundaries for repetition codes and for unmarried parity-check codes are proved, and a few purposes are supplied. because the concentration is at the uncomplicated rules, it considers a binary symmetric resource, binary linear channel codes, and binary-input symmetric memoryless channels. details Combining first introduces the idea that of mutual info profiles and revisits the well known Jensen's inequality. utilizing those instruments, the boundaries on details combining are derived for unmarried parity-check codes and for repetition codes. the applying of the boundaries is illustrated in 4 examples. details Combining offers a very good educational in this very important topic for college students, researchers and rpofessonals operating in communications and knowledge idea.

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Extra info for Information Combining (Foundations and Trends in Communications and Information Theory)

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For SNR → ∞, a single peak at j = 1 remains, pJ (j) = δ(j − 1), and the BIAWGNC, the BEC, and the BSC coincide, of course. 3 Jensen’s Inequality Revisited In this chapter we extend Jensen’s well-known inequality to a simple two-sided bound on the expected value of a convex function of a random variable. Both the upper and the lower bound are tight. First the theorem is revisited, and then the application to mutual information profiles is addressed. , pX (x) = 0 for x = [A, B]. Let f (x) be a real-valued function f : [A, B] → IR which is1 convex-∪ in [A, B].

3. Obviously, for a given mutual information I, the BEC has the MIP with the largest variance possible because the distribution is concentrated at the two ends of the interval [0, 1] for j. The interesting fact that the BSC and the BEC represent the extremes with respect to the variance of J will be of importance when looking for bounds in Chapters 4 and 5. 3 Binary-Input Additive White Gaussian Noise Channel Consider now the BIAWGN channel with quantized output, see Fig. 4. The symbols X ∈ {0, 1} are first BPSK-mapped to the symbols Z ∈ {−1, +1}.

N − 1, and let the complete information on code symbol X0 be defined by Icmp,0 := I(X0 ; Y [0,N −1] ). Then, the following tight bounds hold: par Icmp,0 ≥ fN (I0 , I1 , . . , IN −1 ), Icmp,0 ≤ 1 − (1 − I0 )(1 − I1 ) · · · (1 − IN −1 ). The lower bound is achieved if the channels are all BSCs, and the upper bound is achieved if the channels are all BECs. Note that BSCs achieve the lower bound for repetition codes, but the upper bound for single parity-check codes; the reverse holds for BECs.

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Information Combining (Foundations and Trends in Communications and Information Theory) by Ingmar Land, Johannes Huber


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