Consider a noisy wireless channel which flips each bit (0 becomes 1 or 1 becomes

Question

Consider a noisy wireless channel which flips each bit (0 becomes 1 or 1 becomes 0) with probability p. To guarantee the information is received reliably, each bit is transmitted m times (called repetition coding). For example, if m = 3 and "0" needs to be sent, you transmit "000" instead of "0". Assume m = 3, how many possible sequences the receiver may get? Among these sequences, how many have more "0"s than "1"s? The receiver decodes the information by the majority rule. In other words, the receiver claims the bit is "0" if the received sequence has more "0"s than "1"s. Assume p = 0.3, what is the probability the receiver decodes the bit correctly?

Explanation / Answer

1)

from above table 8 poiaaible sequence the reciver may gets. 4 sequences will have more zeros than 1

The total probapility,1(since only two events are there ,reciver may recive either 0 or 1')=probability of reciver decodes wrongly+probability of reciver decodes correctly

probability of reciver decodes correctly=1-p=1-0.3=0.7

Transmitted bits when m=3 Decoded Bits 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1

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