Question

consider a binary symmetric channel that delivers a transmitted bit correctly with probability 1 − p and flips it with probability p (see fig. 1). consider a repetition code over this channel that transmits every bit n times. in other words, bit 0 is transmitted using codeword 00 . . . 0 | {z } n zeros and bit 1 is transmitted using codeword 11 . . . 1 | {z } n ones . a receiver can detect an error if the received codeword does not match any of these two possible codewords. what is the probability that the error occurs but the receiver is unable to detect it?

Answer 1

Step-by-step explanation:

you would probly send either a 0 or a 1. And the 0 either gets decoded correctly (prob 1-p) or incorrectly (prob p). The same is true for the decoding of 1.