We have derived a new theory of error correction coding. For a given rate, R, we can construct a codeword with greater error correction than that predicted by the traditional theoretical limit. The maximum improvement is 33%. The new theory incorporates the concept of an analytic message or a message with a non-zero level of predictability. We show that error correction is based on both redundancy and predictability and we focus on a special case in which the message is a digital root 9 number.