But then how can you transmit 48123?Īnd if you then add a special delimiter signal to signify that the "8" is a repeat count, then you are adding even more data. E.g., if x = 8888123, you can compress that to four 8s, 123, which is then transmitted as 48123. One reason which I could see as to why RLE or other algorithms can fail would be how to transmit just the plain text. I do understand how some compression algorithms work, such as run-length encoding (RLE), but I cannot see how they avoid this issue. This pattern can then repeat forever showing that without losing any data, any compression algorithm cannot compress data into a size lower than the original input. For compression to be useful there must also be a decode algorithm, d(x), which returns the original input. Because a compression algorithm, c(x), must reduce or keep the same length of the input, then the compressed file must be smaller or equal to the input (and greater or equal to 0). If all data is essentially just a bit string, then all data can be represented as a number.
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