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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

:

The maximum is attained at the capacity achieving distributions for each respective channel. That is,

where is the capacity of the ith channel.

Outline of the proof

The proof runs through in almost the same way as that of channel

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