Sure, I'm assuming that (a) you are trying to encode all strings of length at most n and (b) you have the uniform distribution over those strings. This makes sense in the original context of encoding random data.
>you have the uniform distribution over those strings. This makes sense in the original context of encoding random data.
Lossless compression is nothing more than taking advantage of prior knowledge of the distribution of the data you are compressing.
Random data isn't always (or even often) uniformly distributed. Everything we compress is "random" (in the context of information theory), so I disagree that it makes sense to assume uniformly distributed data.
Then the original statement about not being able to use pi as a data compression method is false. It could be the case that 99% of the time you want to encode the string "141592653".
Lossless compression is nothing more than taking advantage of prior knowledge of the distribution of the data you are compressing.
Random data isn't always (or even often) uniformly distributed. Everything we compress is "random" (in the context of information theory), so I disagree that it makes sense to assume uniformly distributed data.