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The performance of trellis coded modulation (TCM) and bit-interleaved coded modulation (BICM) is compared in wireless LAN systems applying the orthogonal frequency division multiplexing (OFDM). The indoor wireless channel environment is considered, where the channel fades vary very slowly and they are still highly correlated even if the interleavers are applied. The TCM design rules for the additive white Gaussian noise channel (AWGN) and the Rayleigh fading channel are studied, and they are compared with two BICM schemes with the same bandwidth efficiency. It is found that over the very slow flat fading channels, TCM designed for the AWGN channel outperforms TCM designed for the fading channel, and both outperform BICM. Over the very slow multipath fading channels, TCM for the fading channel outperforms TCM for the AWGN channel, and both outperform BICM with the same code rate and signal set. However, BICM with expanded signal set and low-rate code performs better than both TCM schemes.