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Noisy Channel Coding Theorem

13 April, 2015 - 16:56

Let E denote the efficiency of an error-correcting code: the ratio of the number of data bits to the total number of bits used to represent them. If the efficiency is less than the capacity of the digital channel, an error-correcting code exists that has the property that as the length of the code increases, the probability of an error occurring in the decoded block approaches zero.

\lim _{N\rightarrow \infty }Pr \left [Block Error \right ]=0\;,\;E< C