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This paper presents an efficient architecture for a 4-D eight-phase-shift-keying trellis-coded-modulation (TCM) decoder. First, a low-complexity architecture for the transition metric unit is proposed based on substructure sharing. This scheme significantly reduces the required computation without degrading the performance. Then, a new hybrid T -algorithm for a Viterbi decoder is developed by applying a T-algorithm on both branch metrics (BMs) and path metrics (PMs). TCM encoders usually employ high-rate convolutional codes that yield many more transition paths per state than low-rate codes do. This makes it feasible to purge unnecessary additions by applying the T -algorithm on BMs. Applying the T-algorithm on BMs instead of PMs allows one to move the ??search-for-the-optimal?? operation out of the add-compare-select-unit (ACSU) loop. Hence, the clock speed will not be affected. In addition, by combining the T-algorithm on BMs and the T-algorithm on PMs, the hybrid T -algorithm can reduce the computations required with the conventional T-algorithm on PMs by as much as 50%.