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A digital communication system uses a repetition code for channel encoding/decoding. During transmission, each bit is repeated three times (0 is transmitted as 000, and 1 is transmitted as 111). It is assumed that the source puts out symbols independently and with equal probability. The decoder operates as follows: In a block of three received bits, if the number of zeros exceeds the number of ones, the decoder decides in favor of a 0, and if the number of ones exceeds the number of zeros, the decoder decides in favor of a 1. Assuming a binary symmetric channel with crossover probability p = 0.1, the average probability of error is ________?

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Cross over Probability P=0.1 X=number of errors P(error) = (0.5) P(x>=2 @000sent) + (1/2) P(x>=2 @111sent) =2*(1/2)(((3/2)*(0.1)^2 * (0.9)^1))+((3/3)*(0.1)^3 * (0.9)^0)) = 0.028
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