By Andrew J. Viterbi
ISBN-10: 0070675163
ISBN-13: 9780070675162
Written through exotic specialists within the box of electronic communications, this vintage textual content is still an essential source 3 many years after its preliminary book. Its remedy is aimed toward scholars of communications concept and to designers of channels, hyperlinks, terminals, modems, or networks used to transmit and obtain electronic messages. 1979 version.
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Extra resources for Principles of Digital Communication and Coding (Communications and Information Theory)
Sample text
14) we have (du)(L) = 1, while (du)(Y ) = 0, the S 1-form L / X θ is given on the manifold Cu by: L / X θ = L X θ − f du where f = θ ([L, X]). 22) On the other hand, since (Dθ )(Y ) = (L L θ )(Y ) while (Dθ )(L) = 0 = (L L θ )(L), the S 1-form Dθ is given on the manifold Cu simply by: Dθ = L L θ. 23) Again, let Y be an arbitrary S vectorfield. 14). 23), (L / X Dθ )(Y ) = (L X Dθ )(Y ) = (L X L L θ )(Y ). 24) we then obtain / X Dθ )(Y ) = (L L L X θ − L X L L θ )(Y ) = (L[L ,X ] θ )(Y ) = (L / [L ,X ] θ )(Y ).
76) reads −Dζ = −d/ω + χ · ( ζ + d/ ) + β. 69) reads ∇ X Lˆ = ζ(X) Lˆ + χ · X. 30) we have d/ω = Dd/ log , d/ω = Dd/ log . 82) Dη = (χ · η + β). 83) is a propagation equation along the generators of each C u . The S 1-form η may be considered to be the torsion of Su,u with respect to the null geodesic field L , because η(X) = 2 2 g(∇ X L , L ) : ∀X ∈ T Su,u . 84) Similarly, the S 1-form η may be considered to be the torsion of Su,u with respect to the null geodesic field L , because η(X) = 2 2 g(∇ X L , L ) : ∀X ∈ T Su,u .
19) 36 Chapter 1. The Optical Structure Equations with X an arbitrary S vectorfield, holds, and so do the Leibniz rules D(η · θ ) = (Dη) · θ + η · (Dθ ), D(η · θ ) = (Dη) · θ + η · (Dθ ). 20) Let us recall that if X and Y are arbitrary vectorfields and θ an arbitrary tensorfield on any manifold, we have L X LY θ − LY L X θ = L[X,Y ] θ. It then readily follows that if X and Y are S vectorfields and θ an S tensorfield of any type, we have: L / XL /Yθ − L /YL / Xθ = L / [X,Y ] θ. 21) Moreover, we have the following lemma.