MPLS-CE Connected to PE
In this scenario the VPC-SI functions as an MPLS-CE (Customer Edge) network element connected to a Provider Edge (PE) Label Edge Router (LER), which in turn connects to the MPLS core (RFC 4364). See the figure below.

The MPLS-CE functions like a PE router within its own Autonomous System (AS). It maintains Virtual Routing and Forwarding (VRF) routes and exchanges VPN route information with the PE via an MP-eBGP (Multi-Protocol-external BGP) session.
The PE is also configured with VRFs and exchanges VPN routes with other PEs in its AS via MP-iBGP (Multi-Protocol-internal BGP) connections and the MPLS-CE via an MP-eBGP connection.
The EBGP connection allows the PE to change next-hop IP addresses and labels in the routes learned from IBGP peers before advertising them to the MPLS-CE. The MPLS-CE in this case uses only MP-eBGP to advertise and learn routes. Label Distribution Protocol (LDP) and Resource Reservation Protocol (RSVP) are not required because of direct-connect EBGP peering. The MPLS-CE in this scenario pushes/pops a single label (learned over the MP-eBGP connection) to/from the PE.