I am not sure where you get the impression that 3 bits of "quality" are lost. The container still has the original bit depth. But there is now a hidden data channel in which data encrypted as pseudorandom noise can be buried without reducing the original resolution of the audio data,
This is not snake oil or handwaving. Without getting into the specifics of what MQA does, creating a buried data channel takes advantage of the spectral nature of the analog noisefloor present on all music recordings.
I have made several choral recordings since the turn of the century. I always try to make the recording in a quiet hall and spend time chasing down and eliminating sources of noise before the sessions start. My microphones have low self-noise and I use low-noise microphone preamplifiers from Millennia Media. Nevertheless, there is always noise present in the recording.
View attachment 126313
As you can see from this graph, made from a 24-bit recording of the “room tone” in the Oregon church where I made some of these recording, the spectrum of the noise is not flat or “white.” Instead it is closer to pink. The peak level is close to -70dBFS in the low bass (thanks to distant traffic noise) and slopes down at around 24dB/decade to 1kHz and with a somewhat shallower slope in the treble.
An FFT-derived spectrum of dithered 16-bit silence with the same number of FFT bins would produce a flat spectrum with all the components lying around -130dBFS. As the music is always higher in level than the noise, you can see that the only part of the spectrum that would need to be encoded with >16 bits lies between 2kHz and 30kHz. 13 or even 12 bits would be sufficient in the bass.
What this means is that a 24-bit recording of music made in this church that peaks at 0dBFS has spectral space available below the analog noisefloor. If I encode low-bit-depth data of some kind as pseudorandom noise – much easier to write than do - and add it to the 6 or 7 least-significant bits of the original 24-bit audio file, I have created a buried data channel. As the spectrum of that buried data channel is identical to the noisefloor of the recording, I haven’t reducing the resolution of the music data and there is a negligible rise in the overall noisefloor. I haven’t truncated the original 24-bit data to 17 bits or 13 bits or whatever, as has been stated elsewhere in the thread.
You don’t get something for nothing, however. As the noise floor now includes real information, albeit in encrypted form, I have increased the entropy of the file. The data can’t, therefore, be compressed as much by FLAC etc, as the original data.
This is not a new concept. Alan Turing did something somewhat similar in WWII to allow encrypted communication between Winston Churchill and FDR. Turing encoded the voice message as, IIRC, 8-bit audio data then buried it in a recording of random noise. When the message was transmitted, anyone listening would just hear noise. Decoding the message depended on the receiving station having exactly the same recording of random noise. Subtracting the noise signal from the received transmission reconstructed the original voice recording. (For transmission the noise was played from a 78rpm disc and for the system to work, a copy of that disc had first need to be flown across the Atlantic.)
In the 1990s, the late Michael Gerzon worked with Peter Craven (now with MQA) on a similar subtractive dither scheme with a buried data channel intended to increase the resolution of digital audio recordings – see
https://www.aes.org/e-lib/browse.cfm?elib=7964
John Atkinson
Technical Editor, Stereophile