Channel Capacity Theorem


Channel Capacity Theorem

The Shannon theorem states that given a noisy channel with channel capacity C and information transmitted at a rate R, then if R < C  there exist codes that allow the probability of error at the receiver to be made arbitrarily small. This means that theoretically, it is possible to transmit information nearly without error at any rate below a limiting rate, C.
The converse is also important. If R > C, an arbitrarily small probability of error is not achievable. All codes will have a probability of error greater than a certain positive minimal level, and this level increases as the rate increases. So, information cannot be guaranteed to be transmitted reliably across a channel at rates beyond the channel capacity. The theorem does not address the rare situation in which rate and capacity are equal.
The channel capacity C can be calculated from the physical properties of a channel; for a band-limited channel with Gaussian

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