In this paper, we propose a novel compact BDD structure, called Non-crossing ordered BDD (NCOBDD), that can be mapped directly to a regular circuit structure. Compared with other BDD-based regular structures, NCOBDD-mapped circuits reduce the costs of area, power and latency, while preserving the regularity of the structures. We also present an algorithm that uses a top-down level-by-level sweep to construct minimal NCOBDDs. Experimental results show that for asymmetric benchmark circuits, the average reduction on area, power and latency are 61.6%, 53.1% and 69.2%, respectively, compared with Yet Another Decision Diagram (YADD) [9].