QUOTE(riggits @ Aug 29 2005, 12:15 PM)
IOW a codec's idea is to reduce redundancy, filter out inaudibles, and quantize information. So if we take the "difference file" it's going to be essentially random noise, without much chance for compression (and almost zero chance of compression beyond the average lossless codec's ability).
It'd be easier just to use FLAC in the beginning, and save much unnecessary hassle.
I do not agree with that, the enhancement data is more than random noise, a lot more.
PCM audio data is composed by Perceptible signal + non perceptible signal. Each of those signals is composed by entropy (valuable information including the noise) + redundancy (somehow duplicated information).
The perfect lossless audio codec would keep the entropy of the data (entropy of the perceptible signal+entropy of the non perceptible signal) removing only the redundancy.
The perfect lossy audio codec would keep only the entropy of the perceptible signal, removing the whole non perceptible signal and the entropy of the perceptible signal.
The difference between the perfect lossless codec and the perfect lossy audio codec is the entropy of the non perceptible signal, and that info is a big amount of valuable info, about 75% as Nero said in this thread. 75% of a HQ signal it not only noise but also masked sounds, low volume but with a lot of redundancy and insteresting charasteristics such that SLS can achieve lossless compresion of the non perceptible signal with a ratio of 4 to 1. Pure noise would not allow any compression at all and the final lossless is achieved with a ratio of 2.5 to 1, less than compressing only the non perceived signal. Interesting, isn't it? I will not go deeper into this subject since it would be a veeery long dissertation.
@ Megar
Your test is giving us additional info if you analyse the data and the experiment setup. By doing so you can explain why you obtained those values.
1st. MP3 lacks from a good entropy filter so you are not efficiently removing the redundancy of the perceived signal.
2nd. MP3 decoding adds the non perceptible quatization noise under the perceived signal, adding an undesired non perceived entropy to the signal. IOW: you add entropy from the MP3 decoding to the enhancement layer so, as SunHillow suggested, forget about using the Cooledit sustractive method as a valid step.
3rd. FLAC is not a good codec for the enhancement layer since it does not take into account the caracteristics of the non perceptible signal, it means that it is not good enough in removing redundancy either.
You conclude that MP3 + FLAC > Only FLAC since you are adding noise and you are keeping duplicated redundancy in both parts. A better ilustrative codec can be the SLS, where lossy + lossless complement ~= lossless.
Remember the 75% value that Nero said. This value is realistic since the MPEG SLS encoding uses a AAC @ 128Kbps (25% of the total valuable data) as the lossy core codec, very good for this purpose since it has an entropy filter. The enhancement layer achieves lossless compression adding 472 to 572Kbps (75% of the total valuable data), filling this layer with the entropy of the non perceptible signal with an algorithm designed for removing the redundancy of the non perceptible audio signal. The final size is about the same than a lossless only codec like ALS.
Regards,
Oki
Edit1: Finishing the initial post
Edit2: Conclusions about Megar's test