4) Let us consider a block code where b = [b b2 b3 b4] be the...

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4) Let us consider a block code where b = [b₁ b2 b3 b4] be the message and c = [C₁ C2 .........C7] be the codeword, such that C₁ = b₁; C2 = b2; C3 = b3; C4 = b4; b4; b4; C5 b1 b2 = C6 = b₂b3 C7 = b₁b3b4. I. Find the generator matrix. II. Determine parity-check matrix. III. Determine all the codewords of the code. Also show the necessary calculations. IV. Decode the received signal vector 1000101 by computing its syndrome. Show the syndrome vector table (for all error bit positions) required for the identification of error bit. 4) Let us consider a block code where b = [b₁ b2 b3 b4] be the message and c = [C₁ C2 .........C7] be the codeword, such that C₁ = b₁; C2 = b2; C3 = b3; C4 = b4; b4; b4; C5 b1 b2 = C6 = b₂b3 C7 = b₁b3b4. I. Find the generator matrix. II. Determine parity-check matrix. III. Determine all the codewords of the code. Also show the necessary calculations. IV. Decode the received signal vector 1000101 by computing its syndrome. Show the syndrome vector table (for all error bit positions) required for the identification of error bit.