1. Design a feedback shift register encoder for an (8,5) cyclic code with a generator g(x)=1+X+X^2 + X^3. Use the encoder to find the codeword for the message [10101] (20 Marks) in Systematic form. 2. Consider the convolutional encoder shown in Figure 1,
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Step 2: Convert the generator polynomial to systematic form To convert the generator polynomial to systematic form, we need to find the systematic generator polynomial. The systematic generator polynomial is obtained by dividing the original generator polynomial Show more…
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Consider a (15,5) linear block code (cyclic) in systematic form. The generator polynomial is given as g(x) = 1 + X + X^2 + X^5 + X^8 + X^10. Design and draw the circuit of the feedback shift register encoder and decoder. (6 Marks) Use the encoder obtained in part a to find the code word for the message [x x x x x]. (Assume the right most bit is the earliest bit) (5 Marks) Repeat the steps of part b for decoding. (5 Marks) Verify the codeword obtained in part b polynomial division method (5 Marks) Consider a codeword C = [y y y y y y y y y y y y y y y]. Is this a codeword of the above system? Provide suitable justification for your answer. (4 Marks)
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