Is there a way to calculate the actual amount of information in a bit string? Like if you have a 1MB file that losslessly compresses to 1KB, the actual amount of info is <= 1KB. (1/N)
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Replying to @Atrix256
If you have a 1Mb file that losslessly compresses to 1Kb, that must mean that there is a 1Kb file that losslessly "compresses" to be larger than 1Kb. Does that mean the original 1Kb file contains more than 1 bit per bit of information?
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Replying to @uchian
No it doesn't. Compression is an imperfect measure. Actual information is <= compressed size.
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Instead of saying its imperfect I should have said it gives an upper bound
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Technically the upper bound is compressed file size plus the information how to decompress. This is not a big issue for something like LZW, but it is important if you use something like a pre-determimed hamming code for English language ASCII.
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