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In this paper, we studied the necessary and sufficient conditions for Banyan-type networks, which are rearrangeable nonblocking (RNB) by considering all possible degrees of crosstalk constraints. To the best of our knowledge, this paper is the first one to propose a comprehensive solution that takes into account of all the possible crosstalk constraints for optical interconnection network fabrics. Therefore, the necessary and sufficient RNB conditions for optical interconnection networks under various crosstalk constraints are defined completely. Moreover, we found the conditions are independent from the degree of crosstalk constraint. It means the number of needed planes will not increase due to a stricter constraint by allowing a lower degree of crosstalk unless it goes down to zero crosstalk. It also signifies that a much stricter degree of crosstalk constraint could be imposed without changing the hardware fabrics. These conditions provide the useful tips for a cost-effective design of such optical interconnection networks.