Chapter 2: Trellis-Coded Modulation (Ungerboeck)

Learning Objectives

• Construct Ungerboeck's set-partitioning tree for 8-PSK and 16-QAM and read off the intra-subset minimum distances at each level
• State and apply the three Ungerboeck design rules (parallel transitions, common-state transitions, uniform input distribution)
• Derive the asymptotic coding gain formula $\gamma_c = d_{\rm free}^2 / d_{\rm uncoded}^2$ and compute it for the canonical 4-state 8-PSK TCM
• Run one section of the Viterbi algorithm by hand on a 4-state trellis and explain path metrics, survivor paths, and parallel-transition subset decoding
• Explain why TCM revolutionized the V.32/V.34 modems (3–6 dB gain without bandwidth expansion) and why BICM eventually supplanted it in wireless standards