Nonblocking Four-Stage Multicast Network for Multicast-Capable Optical Cross Connects

In this paper, we investigate the four-stage multicast network with only two multicast stages (the second and output stages) being multicast-capable, which is called 4(2 m)-stage multicast network. We first derive the sufficient wide-sense nonblocking (WSNB) and rearrangeable nonblocking (RNB) conditions for the 4(2 m)-stage multicast network. The WSNB and RNB conditions are also presented for multicast request with limited multicast degree. The 4(2 m)-stage multicast network needs at least O(N ^{3 / 2}) crosspoints to be WSNB and RNB, which is a lower bound than the three-stage Clos network with two multicast stages and the same bound with the four-stage network with three multicast stages. Then we design full and partial multicast-capable optical cross connects (MC-OXCs) applying the 4(2 m)-stage multicast network. The proposed WSNB full MC-OXC with two multicast stages is power efficient in reducing splitting loss and has lower multicast cost, compared with the one having three multicast stages. Partial MC-OXC with only one multicast stage is proposed to further reduce the multicast cost and splitting loss. The RNB MC-OXCs with one or two multicast stages provide better performance at the respects of crosspoints, multicast cost, and splitting loss than their WSNB counterparts.