Please check attachment for detail.
1. Consider a code C with generator matrix G given by :
(a) Find the codeword for data (111).
(b) Determine the syndromes of all single bit error vectors.
(c) Determine the syndrome of the received vector r=(0111011) and find the original data.
2. Consider a (7,4) cyclic code generated by g(x)=1+x+x3.
(a) Determine the codeword in systematic form if the message is (111).
(b) With the received vector input to the left end of the syndrome circuit of the Meggitt decoder, use the table below to show the changes in the syndrome register until the entire received vector r=(0110111) has been decoded.
Input Register contents (s0 s1 s2) Correction bit
? ? ? ? ?
(c) Repeat part (b) if the received vector is input to the syndrome register from the right.
3. Consider a (3, 1, 2) convolution encoder with the following impulse responses:
g(1) = (1 1 1)
g(2) = (1 0 1)
g(3) = (1 1 0)
(a) Sketch the block diagram and state diagram of the encoder.
(b) For data input 11011, determine the convolution encoder output.
(c) Use the Viterbi decoding algorithm to decode the received vector:
r = (110, 011, 011, 001, 110, 011, 110)
Draw the trellis diagram and show the discarded paths, cumulative discrepancies and the decoded path.