linear algebra A 4 bit message b = [b_1, b_2, b_3, b_4] is to be sent via a nois
ID: 3013607 • Letter: L
Question
linear algebra
A 4 bit message b = [b_1, b_2, b_3, b_4] is to be sent via a noisy channel. Three parity bits are employed p_1 = (b_1 + b_2 + b_4) mod 2, p_2 = (b_1 + b_3 + b_4) mod 2 and p_3 = (b_2 + b_3 + b_4) mod 2. The message plus parity bits is sent as a 7 bit message c = [c_1, ..., c_7] where c_1 = p_1, c_2 = p_2, c_4 = p_3, c_5 = b_2, c_6 = b_3, and c_7 = b_4. If the message received at the destination is c_rec = [0, 1, 0, 1, 1, 0, 0], what was the original 4 bit message? Assume that there can be at most one erroneous bit.Explanation / Answer
According to the 7 bit message
Data bits are b1 = 0, b2=1,b3=0,b4=0
p1 = 0, p2=1 and p3=1
p1 from the message data = (0+1+0) mod (2) = 1
p2 from the message data = (0+0+0) mod(2) = 0
p3 from the message data = (1+0+0) mod(2) = 1
Hence the only bit which we recieved in error is b1
Hence the correct data packet was 1100 in place of 0100
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