Shannon’s Channel-Coding Theorem

• Definition: Channel capacity

  • The information capacity of a channel is: C = max[I(X;Y)]
  • I(X;Y) = H(X) – H(X½Y) = H(Y) – H(Y½X)

• The Theorem:

  • There is a nonnegative channel capacity C associated with each discrete memoryless channel with the following property: For any symbol rate R < C, and any error rate ? > 0, there is a protocol that achieves a rate >= R and a probability of error <= ?

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