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We introduce source-adaptive shifting (SAS) of modulation signal sets to improve the transmission of source signal samples over a noisy channel. A quantizer is used for source encoding and a non-binary digital modulation scheme for the transmission. As a novelty, the transmitted modulation signal points are shifted away from the ones that are addressed by the quantizer indexes; the goal is to reduce the risk to receive noisy channel outputs within the decision regions of those modulation signal points that are mapped to quantizer levels that cause large distortions in the source signal at the receiver output. The shifts, which depend on the unquantized input source samples, are carried out only at the transmitter; thus, a conventional receiver may be used.