A new class of variable-length uniform random number generators and their asymptotic properties

We propose a new class of variable-length uniform random number generators (URNGs) and investigate their asymptotic properties. It is shown that (i) any variable-length URNG in the class is asymptotically optimal for any given general source, and (ii) the output length of such URNG per source symbol converges in probability to the self-information of the source per source symbol.