AR(1) processes are one of the most popular models in signal processing. Also, stable distributions are good candidates to model sparsity which is in the center of attention of the signal processing community. A basic question about a stochastic process is how much we can decouple it. Finding a domain that results in maximally independent coefficients for stable AR(1) processes has recently been done. In this project we are interested in representations of stable AR(1) processes that has dependencies only within pairs, and the pairs are independent from each other.