A novel compound code is designed for the popular multi-dimensional (M-D) Wei trellis code [1] combined with a simple parity-check code. Using the iterative Viterbi decoding algorithm, we can achieve a remarkable performance improvement with low computational complexity. Simulation results show that at a bit-error-rate (BER) of 3:7  10    about 2.2 dB additional net gain has been obtained over the conventional scheme of the 4-D 16-state Wei code at a spectral eciency of 6.7871 bits/T 