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Constellation constrained (CC) capacity regions of a two-user Gaussian multiple access channel (GMAC) have been recently reported. For such a channel, code pairs based on trellis coded modulation are proposed in this paper with M-PSK and M-PAM alphabet pairs, for arbitrary values of M; to achieve sum rates close to the CC sum capacity of the GMAC. In particular, the structure of the sum alphabets of M-PSK and M-PAM alphabet pairs are exploited to prove that, for certain angles of rotation between the alphabets, Ungerboeck labelling on the trellis of each user maximizes the guaranteed squared Euclidean distance of the sum trellis. Hence, such a labelling scheme can be used systematically to construct trellis code pairs to achieve sum rates close to the CC sum capacity. More importantly, it is shown for the first time that ML decoding complexity at the destination is significantly reduced when M-PAM alphabet pairs are employed with almost no loss in the sum capacity.