Abstract
In this paper, the problem of computing the free distance of TCM code sequences 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 the TCM code sequences has been theoretically solved. The matrix algorithm is derived from the Viterbi algorithm, and is an implementation of the Viterbi algorithm in the form of a matrix. Compared with other algorithms, the matrix algorithm has two advantages: (1) the explicit solution, and its relatively lower complexity, (2) its more reflexible ability to signal space distance variation. As examples, the results of some TCM code sequences on an AWGN channel and fading channels have been presented.
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