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We propose a serial concatenated trellis-coded modulation system using one or more inner rate-1 accumulate codes and a mapping to a higher order, Gray-labeled signal constellation. As outer codes, we consider repeat codes, single parity-check codes, and convolutional codes. We show that under maximum-likelihood decoding, there exists a signal-to-noise ratio threshold beyond which the bit-error probability goes to zero as the blocklength goes to infinity. We then evaluate the performance for finite blocklengths using a modified union bound. Computer simulations demonstrate that the proposed system, despite its use of a simple rate-1 inner code, achieves performance in additive white Gaussian noise and Rayleigh fading that is comparable to, or better than, that of more complex systems suggested in the literature.