von Neumann Correction

Synonyms

De-skewing

Related Concepts

Random Number Generators; Statistical Randomness Tests

Definition

von Neumann Correction is a process for removing bias from pseudo-random bit streams.

von Neumann correction takes pairs of bits as inputs but output bits only when there is a transition in the input bit stream. Because transitions in each direction occur an equal number of times, the bias is eliminated. This comes at the cost of a lower bit rate.

Indeed, let us assume that the source outputs a 1 with probability $\frac{1} {2} + \epsilon$ and a 0 with probability $\frac{1} {2} - \epsilon$. We see that the sequence 11 occurs with probability ${\left (\frac{1} {2} + \epsilon \right )}^{2}$, that the sequence 00 occurs with probability ${\left (\frac{1} {2} - \epsilon \right )}^{2}$ but that the occurrence probabilities of both sequences 01 and 10 are equal to:

$$\left (\frac{1} {2} - \epsilon \right )\left (\frac{1} {2} + \epsilon \right ) = \frac{1} {4} - {\epsilon }^{2}$$

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