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

Prool 

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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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