In this paper, the problem of computing the free distance of Trellis Coded Modulation (TCM) signal sequence has been discussed; a new algorithm-the matrix algorithm is proposed; and the step-number estimation problem for state transmission to compute the free distance of TCM signal sequence has been theoretically solved. The matrix algorithm is derived from the Viterbi algorithm, and is an implementation of Viterbi algorithm in the form of matrix. Compared with other algorithms, the matrix algorithm gains two advantages: (1) The explicit solution, and its relatively less complexity. (2) More reflexible ability to the signal space distance variation. As examples, the results of some TCM signal sequence on AWGN channel and fading channels have been presented.
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