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The capacity of a channel with arbitrarily varying channel probability functions and binary output alphabet

  • R. Ahlswede
  • J. Wolfowitz
Article

Summary

Let X={1,..., a} be the “input alphabet” and Y={1,2} be the “output alphabet”. Let X t =X and Y t =Y for t=1,2,..., X n =\(\mathop \prod \limits_{t = 1}^n \)X t and Y n =\(\mathop \prod \limits_{t = 1}^n \)Y t . Let S be any set, C=={w(·¦·¦)ssS} be a set of (a×2) stochastic matrices w(·∥·¦s), and St=S, t=1,..., n. For every s n =(s1,...,s n )∈\(\mathop \prod \limits_{t = 1}^n \)S t define P(·¦·¦sn)=\(\mathop \prod \limits_{t = 1}^n \)w(y t ¦x t ¦s t ) for every xn=x1, ⋯, xnεXn and every yn=(y1, ⋯, ynYn. Consider the channel C n ={P(·¦·¦)s n s n S n } with matrices (·¦·¦s), varying arbitrarily from letter to letter. The authors determine the capacity of this channel when a) neither sender nor receiver knows sn, b) the sender knows sn, but the receiver does not, and c) the receiver knows sn, but the sender does not.

Keywords

Stochastic Process Probability Theory Probability Function Mathematical Biology Stochastic Matrice 
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 1970

Authors and Affiliations

  • R. Ahlswede
    • 1
  • J. Wolfowitz
    • 2
  1. 1.Ohio State UniversityColumbusUSA
  2. 2.Dept. of MathematicsUniversity of IllinoisUrbanaUSA

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