t the transmit- ter side and correct bit errors along the way. Chapter Eight Problems 1. You want to build a TCM system that is to use the convolutional coder of Figure Q8.1 and the modulation scheme of Figure Q8.2. (a) Draw the trellis diagram representing the convolutional coder. (b) Assign modulation symbols to output bits by using mapping -by -set -partitioning. Provide a complete trellis diagram including modulation outputs. (c) Draw the TCM decoder front end. (d) Given A = 1 and that the output of the TCM decoder front end is (0.7, 0), (1.2, 0), (3.3, 0), (1.2, 0) use the Viterbi Algorithm to determine the output of the TCM decoder. Figure Q8.1 Convolutional coder 2 bits input 3 bits output O2 (t) Figure Q8.2 8 outputs of modulator 01(t) Trellis-Coded Modulation (TCM): The Wisdom of Modulator and Coder Togetherness 2. Consider the convolutional coder of Figure Q8.3. Assume that the modulation is 32-ASK. Using your understanding of trellis diagrams and mapping-by-set partitioning, draw a trellis diagram that includes the output of the modulator. Figure Q8.3 Convolutional coder input bits output bits 3. Provide a trellis diagram and a block diagram that fully describes a TCM coder meeting the following criteria: The channel coder must have 1 bit input and 2 bits output; The modulation scheme must be QPSK. 4. Describe the benefits of using the TCM of Figure Q8.1 in place of using the same convolutional coding followed by a 4-PSK modulator. Chapter Channel Filtering and Equalizers Chapter 5, we talked about using modulators to map bits m to a signal s(t) that could be sent over the channel. We saw that the channel added a noise (t) to the sent signal, giving the receiver the noisy r(t) = s(t) + n(t). We took this a step further when we talked about demodulators, which, given r(t) = s(t) + n(t), did their best to regenerate the original bit sequence m. Now we take this even further. This time we'll consider something called pulse shaping at the modulator. Modulators still take bits m and turn them to a signal s(