An audio coding scheme allowing PCM signal to lossless DSD signal expansion for next generation optical disc formats. The method of encoding an input DSD signal includes up-sampling a corresponding PCM signal to the DSD sample rate. Then a set of loop filter parameters for a noise-shaping loop of a sigma-delta modulator are generated, either using a random starting condition of the sigma-delta modulator or including synchronization parameters. This will allow a decoder to regenerate an almost perfect signal, but still it needs a correction signal to be able to bit identically regenerate the DSD input signal. Therefore, a correction signal is generated based on a difference between a sigma- delta modulated version of the up-sampled PCM signal and the input DSD signal, wherein the sigma-delta modulated version of the up-sampled PCM signal is obtained using the set of loop filter parameters. The correction signal may be adapted to be applied to the low bit PCM signal, to the up-sampled PCM signal or to the output bit stream. Finally, an expansion bit stream is generated where an encoded version of the set of loop filter parameters and an encoded version of the correction signal are included. The decoder can reproduce the original DSD signal based on the already available PCM signal and the described expansion bit stream. Thus, the coding scheme enables top quality audio with minimal storage overhead since the already available PCM signal is used in combination with an expansion bit stream. Since only an additional data stream is required to be stored on a disc, e.g. as part of an MPEG stream, DSD functionality is added to existing systems without causing compatibility problems.