 Decoding: Part 2-Convolutional Coding and Decoding Problems 1. Draw the trellis diagram for the k = 1, n = 3, K = 3 convolutional coder de- scribed by g(1)=1+X+X (Q7.1) g2(X)=1+X = (Q7.2) g3(X)=1+X2 (Q7.3) 2. Draw the trellis diagram for the convolutional coder described by Figure Q7.1. Figure Q7.1 Convolutional coder 3. Given the trellis diagram of Figure Q7.2, determine its block diagram. Figure Q7.2 Trellis diagram 4. Consider the convolutional coder (k = 1, n=2, = K=3) = shown in Figure Q7.3. Use the Viterbi Algorithm to determine the output of the convolutional decoder when it receives (10 00 00 10 11). Chapter Seven Figure Q7.3 Convolutional coder 5. Consider the convolutional coder in Figure Q7.4. Use the Viterbi Algorithm to determine the convolutional decoder output given its input is (11 01 01 10 01). Figure Q7.4 Convolutional coder 6. Consider the convolutional coder (k=1) of Figure Q7.5. (a) Determine n and K. (b) Describe the convolutional coder using a trellis diagram. (c) Assume the signal received by the convolutional decoder is 00 01 00 01. Determine, using the Viterbi Algorithm, the output of the decoder. (In cases of ties at a node, always assume the top path wins.) Figure Q7.5 Convolutional coder 7. Draw the trellis diagram for the convolutional coder in Figure Q7.6. Determine if this convolutional coder is catastrophic. If it is, show (using the trellis diagram) how a finite number of errors in the channel can cause an infinite number of errors at the convolutional coder. Channel Coding and Decoding: Part 2-Convolutional Coding and Decoding Figure Q7.6 Convolutional coder 8. (a) Build any rate 1/2 convolutional coder (do not use one of the ones already used in the problem set or the one used in the text). (b) Describe it using a trellis diagram. (c) Explain in three to four sentences how the convolutional decoder works. (d) Determine if the convolutional coder you built was catastrophic. Chapter Trellis-Coded Modulation (TCM) The Wisdom of Modulator and Coder Togetherness igure 8.1 shows a c