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Degraded Broadcast Channels

  • Jacob Wolfowitz
Conference paper
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 31)

Abstract

Let A = {1,..., a}, B = {1,..., b}, and C = {1,..., c}. Let w1(· | ·) be the c.p.f. of a d.m.c. A → B, and w2(· | ·) the c.p.f. of a d.m.c. B → C. Write A n * for the Cartesian product of n A’s, with similar definitions for B n * , C n * , and, later, for D n * . There are three individuals I, II, III who act as follows: I wishes to send to II an arbitrarily chosen pair (i, j) of messages over the d.m.c. w1(·|·), and the message j to III over the d.m.c. w3(·|·), where
$$ {\omega _3}\left( {{s_2}\left| {{s_1}} \right.} \right) = \sum\limits_{s = 1}^b {{\omega _2}} \left( {{s_2}\left| s \right.} \right){\omega _1}\left( {s\left| {{s_1}} \right.} \right) $$
$$ 1\underline{\underline < } \,{s_1}\underline{\underline { < \,}} \,a,1\underline{\underline < } \,{s_2}\underline{\underline < } \,c $$
.

Keywords

Markov Chain Similar Definition Random Code Rate Pair Chance Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Jacob Wolfowitz
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

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