Would it be possible to convert a lossy format , say MP3 128kbps to AAC 128kbps without loss, i know it isnt at the moment.
The way it works at the moment is that the encoder will convert source file to PCM then reencode to the desired size/codec resulting in loss of quality but i wonder if a program could be written that would analyze the MP3 and create a duplicate in another codec without conversion to pcm, the outputed file would have to be the same bitrate or higher than the source.
I imagine some sort of mapping algorithm between the two codecs.
I know this is speculation but i just wondered if it could be done...

From the nature of lossy encoding, the answer has to be no. It doesn't matter if you go through wave format or not.
You could maybe rephrase to "minimal loss" or search for "transcoding".

From this bitrate range and between these two formats (MP3 -> AAC) it's more than clear that transcoding will have a great quality loss.

Some state that transcoding from Musepack Q8 and above is not an issue though.

I've had nothing but abysmal results transcoding from 128k in various combos to various formats. Talking about mp3 I've tested several samples through abx tests recently. I would say that that 256k is the bare minimum for transcoding. At 320k quality is excellent and largely transparent going from mp3 > mp3 as well as to other formats. IMO MP3 320k is a better solution than MPC due to the huge software and hardware support for 320k file and the robust re-encoding quality.

Theoretically speaking, I think it's possible. If it's possible in practice depends on the actual formats, and even if it is, it would be a lot of work, for a program that won't be useful to a lot of people IMO. I don't expect such a program will be developed, unless someone has a serious overdose of spare time.

Discussed dozens of times already. Summary: Purely theoretically, it would be possible. Practically however it is too difficult to achieve - thus, in practice it is NOT possible.

Posters are correct that this specific configuration is a no-go. The source is of low quality (128kbps MP3) and the transcoding is likely to exacerbate the artifacts.

But other configurations may give acceptable results. For example, I have transcoded 128kbps Protected AAC files (from the iTunes Store) to MP3 using LAME -v2 settings with very good results - the files are a bit larger but little is lost from a practical perspective. ABXs of most tracks reveal no useful difference. This is essentially "up transcoding" to a higher bitrate, and I consider this useful for instances where the original files cannot be used. In this case, I needed unprotected versions of the tracks for use on my work computer.

Likewise, going from a high quality MP3 source (e.g. LAME -v2) to AAC 128kbps is usually not too bad in my experience. I have used this to get more tracks on my older iPod Shuffle and it works surprisingly well with few noticeable artifacts.

Oddly, some combinations don't work well but I don't know why. One example I have found is transcoding from large AAC to small AAC; I have some 192kbps AAC tracks that I wished to reduce to 128kbps for the Shuffle, and found that the artifacts were VERY noticeable. I suspect this has to do with the details of the algorithm, but I have not spent much time investigating. I wonder if using iTunes VBR would help...?

Answer: Stick to the original lossy file. There would be no gain in transcoding mp3 to AAC other than to maybe satisfy some kind of OCD complex.
JXL