Consider the following Convolutional code: $G_1(x) = 1 + x^2$ $G_2(x) = 1 + x^1 + x^2$ a) If the input for this decoder is: 1 0 1 1 1 0 0, what is the encoded codeword? Input: 1 0 1 1 1 0 0 Output:
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FORWARD ERROR CORRECTION CODING AND DECODING y0(n) = x(n) ⊕ x(n-1) ⊕ x(n-2) x(n) D D x(n-1) x(n-2) y1(n) = x(n) ⊕ x(n-2) Input Sequence: 0 1 0 1 1 1 0 0 1 0 1 0 0 0 1 (15 bits) + 0 0 (2 encoder TAIL bits) (17 bits) Encoder State: {x(n-1) x(n-2)} Figure 2.11: Example Convolutional Encoder for Viterbi Decoding Refer to the encoder. What is the code rate?
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