I've seen a few topics/posts recently about various types of improvements that might be possible with both lossless and lossy codecs - in particular people wondering if we have hit some brick wall in terms of compression potential.

I thought it might be interesting and valuable to break down the popular codecs by their various compression phases, identifying which of these phases (perhaps) has more potential than others for improvement. Just to make clearer what I'm talking about: the original audio signal may pass through several processing phases on its way to being "fully" compressed, with some of these phases being: resampling, bit-depth reduction, frequency filtering, psycho-acoustic filtering, inter-channel re-statement, predictor/error processing, and typically some form of entropy encoding (this list is not exhaustive).

I've seen a brief discussion about MP3 some while back along these lines but could not find it by searching.

In terms of quantifying such a break down, perhaps a measure of "phase compression" would be useful: what is the ratio of bit-reduction that a phase may offer (outgoing/incoming bits, expressed as a percentage)?

I'm not in a position to offer such a breakdown for any codec, but many folk here are...

This might belong in a technical forum, I'm not sure, BUT I think that the idea of perceptual coding is getting pretty well exhausted.

http://www.aes.org/sections/pnw/ppt.htm and go to the "perceptual coding tutorial". It's quite a few years old, but the basics, as far as I know, aren't at all changed.

Luckily there's still room for discussion about how far the bitrate can/should be increased before the difference becomes inaudible and which formats are best suited for the job.
Quite a few hi-res topics have come back to life recently so it seems that at least some readers are interested.