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Joint source and channel (JSC) coding using combined trellis coded quantization (TCQ) and continuous phase modulation (CPM) is studied. The channel is assumed to be the additive white Gaussian noise (AWGN) channel. Optimal soft decoding for JSC coding using jointly designed TCQ/CPM is studied in this paper. The soft decoder is based on the a posteriori probability (APP) algorithm for trellis coded CPM. It is shown that the systems with soft decoding outperform the systems with hard decoding especially when the systems operate at low to medium signal-to-noise ratio (SNR). Furthermore, a TCQ design algorithm for the noisy channel is developed. It has been demonstrated that the combined TCQ/CPM systems are both power and bandwidth efficient compared with the combined TCQ/TCM/8PSK systems. The novelty of this work is the use of a soft decoder and the APP algorithm for combined TCQ/CPM systems.