Generation of correlated binary sequences from white noise

We suggest a method for generation of random binary sequences of elements 0 and 1, with prescribed correlation properties. It is based on a modification of the widely used convolution method of constructing continuous random processes. Using this method, a binary sequence with a power-law decaying pair correlator can be easily generated.

Figure 1

(Color online) Correlation function of the binary sequence with power-law decaying correlations. The inset shows the correlation function with alternating sign. Solid circles are for the theoretical formulas Eq. (23), and open circles are for the numerical data for generated sequences of length ${10}^5$. The value $K\left(0\right)=1$ is not shown.