[Computeiful]

It does seem possible, e.g. rather than sending an uppercase alphabetic message as 8-bit ASCII bytes, you can send their position in the alphabet instead, so 01000001 becomes 00001.

Of course this only works when you're limiting yourself to a subset of all possible data (in this case, the uppercase alphabet). A general method where all possible binary combinations are indexed (and the indexes are sent rather than the data) would not save any data as the binary data would always be its own index.