Shannon's theorem has wide-ranging applications in both communications and data storage. This theorem is of fundamental importance to the field of information theory. 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 channel capacity C can be calculated from the physical properties of a channel; for a band-limited channel with Gaussian noise, using the Shannon-Hartley theorem.