Efficient digital transmission of analog speech, audio or video requires source coding which introduces unavoidable quantization errors. The bit stream produced by the source encoder needs to be protected against transmission errors by channel coding. The split of a given gross bit rate between source and channel coding is a compromise taking into account the design target of the worst case channel. Thus, even in clear channel conditions the quality of the decoded source signal is limited because of the quantization errors. Hybrid digital-analog (HDA) codes address this limitation by additionally transmitting the quantization error with quasi-analog methods (discrete-time, quasi-continuous-amplitude) with neither increasing the transmit power, nor the occupied frequency bandwidth on the radio channel. However, the decoding complexity of existing HDA codes is infeasible for the required block lengths. In this paper, the decoding complexity problem is solved by a new design approach. These HDA codes benefit from well-known digital codes. Furthermore, theoretical bounds are derived and explicit guidelines for the design of superior HDA systems are given. By experimental verification it is shown that the HDA concept may outperform conventional purely digital transmission systems at all channel qualities while additionally eliminating the quality saturation effect.