2. The binary 3-fold repetition code is to be used for one of two possible channels. The first is a non-symmetric channel wh ich induces 1 --+ 0 errors with probability a and 0 -+ 1 errors with probability ß. The seeond is asymmetrie ehannel with an overall symbol error probability equivalent to that of the first ehannel, !(a + ß). The ehannel is to be used in 1-error-eorrecting mode. If P(sym) and P(non - sym) denote the probabilities that a word is wrongly deeoded using the respeetive ehannels, show that, provided 000 and 111 are equally likely to be sent, 3 P(sym) - P(non - sym) = 4"(a - ß)2(a + ß - 1).

Henee decide what other information is needed in order to decide whieh ehannel to use.