ginator to recipient. As previously established, the effect of channel noise is to increase the uncertainty in the recipient source Y, as translated by the entropy inequality H(Y) > H(X) with respect to the input source entropy H(X). As also observed, this increase of uncertainty does not correspond to additional information. Rather, it corresponds to an uncertainty in the effective transmission of information from originator to recipient. In noisy symmetric channels, the transition matrix P(Y)X) is different from identity, which means that there is no deterministic (or one-to-one) correspondence between the input symbols Xi and the output symbols y. Short of this unique correspondence between input and output symbols, any received message (i.e., sequence of symbols) is likely to be corrupted by a finite amount of symbol errors. Given Xi as input, a symbol error is defined as any discrepancy between the recipient output symbol yi, which would have been expected with certainty in a noiseless channel, and the symbol y+ actually output by the recipient. For messages of sufficient size (or number of symbols), the mean error count is called the symbol error rate (SER). Let us now formalize the SER concept. Given the fact that the two sources X, Y have equal size N, there exists a one-to-one symbol correspondence Xi yi between them. To each input message or input symbol sequence XiXjXk... thus, corresponds a unique output message or output symbol sequence YiYjYk, of matching size, in which each symbol is the faithful counterpart of the symbol of same rank in the input sequence. With the noisy channel, any error concerning the received symbol yi corresponds to the joint event (vj,xi#j). The probability associated with this specific symbol error is p(yj,xij). The total channel SER is given by the sum of all possible symbol error probabilities according to: (12.19) 1 (,). 12.4 Symbol error rate The second line in Eq. (12.19) expresses the fact that the SER is the probability of the event complementary to that of the "abso