Well, if you have one pseudo random number generator in your library that describes let's say 80% of the bits of the sequence in the block without error, the compressed diff will take care of the error correction. Of course at even at 80% accuracy we only perhaps achieve a mere 5 to 1 compression ratio. To get 100 to 1, we'd have to get into the 99% realm.
I have no clue as to how many pseudo random nubmer generators would be needed in the library to describe all the possible data out there with 99% accuracy, but it's definitely not infinite though it may be astronomically large.
Hmm...pseudo random number generators exhibit chaotic behavior, thus while they appear to be random, they can be modeled by some non-linear model. Perhaps this is where the high dimesional analysis in the press release they mention comes in.
Actually I think something can be done without breaking what you just proved.
If I remember correctly, these guys claim to use randomness to their advantage. Here's my guess into how randomness can be used. It's a complete shot into the dark.
Given a block of random sequence of bits and a library of pseudo-random number generators that generates 1's and 0's with equal probability:
1. Find a pseudo-random number generator and the seed that generates a sequence that best approximates the block given (i.e. a sequence that has low number of differences with the input)
2. Take the diff of the two sequences and compress the diff with standard lossless compression (e.g. Huffman encoding)
3. We now can represent that block by some ID representing the pseudo-random number generator, the seed, and the compressed diff.
The catch is that both sides must have the same library of pseudo-random number generators. Thus in essence, that libary serves as a code book used to encode the block. The diff is there to make the approximation process less cumbersome.
I just thought of this off the top of my head and haven't done any rigorous thinking about it. So I have no clue whether this would work or not. Any one think this would work?
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Well, if you have one pseudo random number generator in your library that describes let's say 80% of the bits of the sequence in the block without error, the compressed diff will take care of the error correction. Of course at even at 80% accuracy we only perhaps achieve a mere 5 to 1 compression ratio. To get 100 to 1, we'd have to get into the 99% realm.
I have no clue as to how many pseudo random nubmer generators would be needed in the library to describe all the possible data out there with 99% accuracy, but it's definitely not infinite though it may be astronomically large.
Hmm...pseudo random number generators exhibit chaotic behavior, thus while they appear to be random, they can be modeled by some non-linear model. Perhaps this is where the high dimesional analysis in the press release they mention comes in.
Actually I think something can be done without breaking what you just proved.
If I remember correctly, these guys claim to use randomness to their advantage. Here's my guess into how randomness can be used. It's a complete shot into the dark.
Given a block of random sequence of bits and a library of pseudo-random number generators that generates 1's and 0's with equal probability:
1. Find a pseudo-random number generator and the seed that generates a sequence that best approximates the block given (i.e. a sequence that has low number of differences with the input)
2. Take the diff of the two sequences and compress the diff with standard lossless compression (e.g. Huffman encoding)
3. We now can represent that block by some ID representing the pseudo-random number generator, the seed, and the compressed diff.
The catch is that both sides must have the same library of pseudo-random number generators. Thus in essence, that libary serves as a code book used to encode the block. The diff is there to make the approximation process less cumbersome.
I just thought of this off the top of my head and haven't done any rigorous thinking about it. So I have no clue whether this would work or not. Any one think this would work?