A general formula for channel capacity

  • Authors:
  • S. Verdu;Te Sun Han

  • Affiliations:
  • Dept. of Electr. Eng., Princeton Univ., NJ;-

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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Abstract

A formula for the capacity of arbitrary single-user channels without feedback (not necessarily information stable, stationary, etc.) is proved. Capacity is shown to equal the supremum, over all input processes, of the input-output inf-information rate defined as the liminf in probability of the normalized information density. The key to this result is a new converse approach based on a simple new lower bound on the error probability of m-ary hypothesis tests among equiprobable hypotheses. A necessary and sufficient condition for the validity of the strong converse is given, as well as general expressions for ε-capacity