Noisy-channel Coding Theorem - Channel Coding Theorem For Non-stationary Memoryless Channels

Channel Coding Theorem For Non-stationary Memoryless Channels

We assume that the channel is memoryless, but its transition probabilities change with time, in a fashion known at the transmitter as well as the receiver.

Then the channel capacity is given by

C=\lim \inf \max_{p^(X_1),p^(X_2),...}\frac{1}{n}\sum_{i=1}^nI(X_i;Y_i).

The maximum is attained at the capacity achieving distributions for each respective channel. That is, C=\lim \inf \frac{1}{n}\sum_{i=1}^n C_i where is the capacity of the ith channel.

Read more about this topic:  Noisy-channel Coding Theorem

Famous quotes containing the words channel, theorem and/or channels:

    “The Xanthus or Scamander is not a mere dry channel and bed of a mountain torrent, but fed by the ever-flowing springs of fame ... and I trust that I may be allowed to associate our muddy but much abused Concord River with the most famous in history.”
    —Henry David Thoreau (1817–1862)

    “To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
    —Albert Camus (1913–1960)

    “Not too many years ago, a child’s experience was limited by how far he or she could ride a bicycle or by the physical boundaries that parents set. Today ... the real boundaries of a child’s life are set more by the number of available cable channels and videotapes, by the simulated reality of videogames, by the number of megabytes of memory in the home computer. Now kids can go anywhere, as long as they stay inside the electronic bubble.”
    —Richard Louv (20th century)