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:

    “This is what the Church is said to want, not party men, but sensible, temperate, sober, well-judging persons, to guide it through the channel of no-meaning, between the Scylla and Charybdis of Aye and No.”
    —Cardinal John Henry Newman (1801–1890)

    “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)

    “People between twenty and forty are not sympathetic. The child has the capacity to do but it can’t know. It only knows when it is no longer able to do—after forty. Between twenty and forty the will of the child to do gets stronger, more dangerous, but it has not begun to learn to know yet. Since his capacity to do is forced into channels of evil through environment and pressures, man is strong before he is moral. The world’s anguish is caused by people between twenty and forty.”
    —William Faulkner (1897–1962)