Let’s say we want to mix three channels onto two because the communication device has only two available channels but we still want to emulate a three channel link. If we can afford coding, then it’s not a problem because we can build our own protocol so add any number of channels using a structured data stream. But what if we cannot control the channel coding at all? In CDs, for example, there’s no coding: there are two channels encoded in PCM and a standard CD player wouldn’t understand the sound if it was encoded otherwise.
The solution is to mix the three channels in a quasi-reversible way, and in a way that the two channels can be listened to without much interference. One possible way is to mix the third channel is to use a phase-dependant encoding. Early “quadraphonic” audio systems did something quite similar. You can also use a plain time-domain “mixing matrix” to mix the three channels onto two. Quite expygeously, let us choose the matrix: