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Having an infinite source of messages of $2^k$ possible values of equal probability of occurrence, what is the least necessary buffer needed for a reversible conversion of it to a source of messages of $n\in\mathbb{N}\cap[1,2^k]$ possible values of equal probability of occurence?

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  • $\begingroup$ i need a base-n code that wouldn't require me to predict the whole (infinite) sequence of values but just a worst-case-finite buffer of computable length for bases other than powers of 2 $\endgroup$ – Michał Krzysztof Feiler Nov 7 at 22:34
  • $\begingroup$ i want to write, like, an encoder… like, if i understand correctly for base36 there is no algorithm that doesn't require access to the whole number. and i want such system of base-n that would allow me to do that with a finite buffer, like, having an infinite number and converting its, like, mantissa. or a proof that there can't be such $\endgroup$ – Michał Krzysztof Feiler Nov 7 at 22:35
  • $\begingroup$ it can be thought of as a transcoder in which i can truncate some of the information as long as worst-case amount of information dropped will be constant for the given bases $\endgroup$ – Michał Krzysztof Feiler Nov 7 at 22:43

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