The design of a source-controlled turbo coding scheme for the transmission of strongly nonuniform binary memoryless sources over additive white Gaussian noise (AWGN) channels is considered. The use of nonbinary signaling allows performance improvements over previous existing schemes that use binary modulation. The basic idea is to allocate more energy to the transmitted symbols associated with the information bits that occur less likely and to exploit the source nonuniformity in the decoding process. If the source and channel parameters are unknown, they can be estimated jointly with the encoding/decoding process. No performance degradation is observed in this case.