In this paper, the problem of optimally communicating analog sources using a bandwidth and power limited digital system is considered. We propose and analyze optimal combined source-channel coding schemes that jointly optimize the compression of the source while controlling the individual bit error probabilities to minimize the mean-squared distortion in reconstructing the signal. For a spectrally shaped channel, the proposed schemes are most efficiently implemented using multicarrier modulation. We optimize the power allocation across subchannels and the constellation within each subchannel. The results indicate that the optimal power allocation is not achieved by a water-filling solution and significant gains (several dB) can be obtained by our optimal design.