- Is this really feasible as the authors suggest it? According to the paper, their results are very efficient and always compress data to a smaller size. Won't the dictionary size be enormous?
Yes, of course. Even for their hand-picked example ("THE QUICK SILVER FOX JUMPS OVER THE LAZY DOG"), they don't achieve compression, because the dictionary contains every 4-byte substring of the text (minus 4 bytes for the one repetition of "THE")... and the "compressed" version of the text has to include the whole dictionary plus all this prime number crap.
- Couldn't this be used to iteratively re-compress the compressed data using the same algorithm? It is obvious, and has been demonstrated, that such techniques (where the compressed data is re-compressed as many times as possible, dramatically reducing the file size) are impossible; indeed, there would be no bijection between the set of all random data and the compressed data. So why does this feel like it would be possible?
Again you seem to have a good intuitive grasp of the situation. You have intuitively realized that no compression scheme can ever be effective on all inputs, because if it were, we could just apply it over and over to compress any input down to a single bit — and then to nothingness!
To put it another way: Once you've compressed all your .wav files to .mp3, you're not going to get any improvement in file size by zipping them. If your MP3 compressor has done its job, there won't be any patterns left for the ZIP compressor to exploit.
(The same applies to encryption: if I take a file of zeroes and encrypt it according to my cryptographic algorithm of choice, the resulting file had better not be compressible, or else my encryption algorithm is leaking "pattern" into its output!)
- Even if the technique is not perfect as of yet, it can obviously be optimized and strongly improved. Why is this not more widely known/studied? If indeed these claims and experimental results are true, couldn't this revolutionalize computing?
These claims and experimental results are not true.
As Tom van der Zanden already noted, the "compression algorithm" of Chakraborty, Kar, and Guchait is flawed in that not only does it not achieve any compression ratio, it is also irreversible (in mathspeak, "not bijective"): there are a multitude of texts that all "compress" to the same image, because their algorithm is basically multiplication and multiplication is commutative.
You should feel good that your intuitive understanding of these concepts led you to the right conclusion instantly. And, if you can spare the time, you should feel pity for the authors of the paper who clearly spent a lot of time thinking about the topic without understanding it at all.
The file directory one level above the URL you posted contains 139 "papers" of this same quality, all apparently accepted into the "Proceedings of the International Conference on Emerging Research in Computing, Information, Communication and Applications." This appears to be a sham conference of the usual type. The purpose of such conferences is to allow fraudulent academics to claim "publication in a journal", while also allowing unscrupulous organizers to make a ton of money. (For more on fake conferences, check out this reddit thread or various StackExchange posts on the subject.) Sham conferences exist in every field. Just learn to trust your instincts and not believe everything you read in a "conference proceeding", and you'll do fine.