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

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