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A reduced-complexity modified decoding algorithm for turbo trellis-coded modulation (TTCM) is proposed and evaluated in terms of complexity and bit error rate (BER) performance in an additive white Gaussian noise channel. The algorithm uses an optimal approximation of the Jacobian logarithm, used in the so-called Log-MAP decoding, by means of the max operation and three piecewise-linear terms. Further computational complexity savings are obtained by applying this approximation only to the two largest values within the decoding step. To improve performance, the algorithms are also investigated using a scaling factor for the extrinsic information. Computer-simulated BER performance evaluation results and complexity comparisons are reported showing the near-optimal performance as well as noticeable implementation advantages of the proposed algorithms with respect to the Log-MAP decoding.