Download e-book for kindle: Advances in Electronics and Electron Physics, Vol. 79 by Peter W. Hawkes (Ed.)

By Peter W. Hawkes (Ed.)

ISBN-10: 0120146797

ISBN-13: 9780120146796

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Extra resources for Advances in Electronics and Electron Physics, Vol. 79

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Mapping by set partitioning works best when IS1 is small (IS1 < 32). A simple method of extending set partitioning to trellis codes with large I UI and IC1 is to use partial uncoded modulation. In this method, the output of the encoder selects a “coset” of the constellation rather than an individual point. Several uncoded bits bypass the encoder to choose a point from the selected coset. In effect, the uncoded bits act as parallel transitions in the trellis diagram. Figure 18 shows two equivalent representations of the same code: one with parallel transitions, and one without.

U k =g(so, u o " ' u k - I ) . 1) (34) (35) Although the above description is time-invariant, periodic or cyclic behavior is possible. G. B. Trellis Diagrams A trellis diuyram is a graphical tool depicting the state transition and output functions of a trellis code. Trellis diagrams are bulky and inconvenient, especially when IS1 is large. However, they clearly illustrate any symmetries in the state-transition function, and they are useful for heuristically designing small trellis codes. 20 HOWARD J.

Y L ) = u if ML(u,u o . " u L - = ( y o , .. ,y L )for some u, uo,. . ,uL- E U. Otherwise, assign KL(y0,.. ,y L )any arbitrarily chosen u E U. Using this mapping, the L -delay inverse system is + uk = sk +1 KL(yk c(s;l = b(Uk) )? Yk+ 1 c(a(s;')),. . yk t L C(aL(sk'1)) 9 * a(sk). (71) (72) Although the inverse of an LSC is always an LSC, the inverse of an FGH is not always an FGH because KL need not be a homomorphism. F. Catastrophic Codes and Injinite Input Memory Systems Catastrophic error propagation is a topic closely related to the construction of inverse systems.

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Advances in Electronics and Electron Physics, Vol. 79 by Peter W. Hawkes (Ed.)

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