For flexibly signaling a synchronous mode or an asynchronous mode in the multi-channel parameter reconstruction, a parameter configuration cue is inserted in the data stream, which is used by a configurator on the side of a multi-channel decoder to configure a multi-channel reconstructor. If the parameter configuration cue has a first meaning, the configurator will look for further configuration information in its input data, while, when the parameter configuration cue has another meaning, the configurator performs a configuration setting of the multi-channel reconstructor based on information on a coding algorithm with which transmission channel data have been coded, so that it is ensured efficiently on the one hand and flexibly on the other hand that there will always be obtained a correct association between parameter data and decoded transmission channel data.