I have a sequence of numbers $x_1, x_2, \dots, x_n, \dots \in \mathbb{R}$ I would like to extract fair bits from that sequence.
My first thought was to use the Von Neumann extractor. For a sequence of 0 and 1,
- divide sequence into pairs
- eliminate all occurrences of 00 and 11
- apply transformation 01 → 1 and 10 → 0
This produces a sequence of fair bits from biased bits *even if you do not know the bias $p = \mathbb{P}[x_i = 1]$ as long as your sequence is
- a Bernoulli trial
- independently distributed
- identially distributed
The sequence of numbers I have is the hourly readings from a sensor, so it exhibits cyclic behavior every 24 hours + every week. If I compute the expected value over time, it may be possible to subtract out the daily and weekly cycles leaving sequence of loosely self-correlated real numbers.
How can I extract randomness from here in a simple way?
0
and1
) but they are not identically distributed. $\endgroup$ – john mangual May 25 '14 at 11:55