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

  • R. Ahlswede
  • J. Wolfowitz


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.


Stochastic Process Probability Theory Probability Function Mathematical Biology Stochastic Matrice 
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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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