Joint channel estimation and decoding using belief propagation on factor graphs requires the quantization of probability densities since continuous parameters are involved. We propose to replace these densities by standard messages where the channel estimate is accurately modeled as a Gaussian mixture over multipah channel. Upward messages include symbol extrinsic information and downward messages carry mean values and variances for the Gaussian modeled channel estimate. Such unquantized message propagation leads to a complexity reduction and a performance improvement. Over multipath channel, the proposed belief propagation almost achieves the performance of iterative APP equalizer and outperforms MMSE equalizer.