GATE 2016 EC – Question 59
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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Correct answer: 0.025 to 0.030
Explanation
The decoder makes a mistake when at least 2 of the 3 bits are flipped. The probability is $3p^2(1 - p) + p^3 = 3(0.01)(0.9) + 0.001 = 0.027 + 0.001 = 0.028$.