Cloud computing has been recognized as an important advance for virtualizing computing hardware, distributed computing middleware, and communication networks. For simplifying the network OA&M (Operation, Administration, and Management) tasks of customers, a CaaS (Communications-as-a-Service) operator can provide virtual communication channels tailored for delivering various services inside a communication cloud, such as VoIP, video conferencing and IPTV. For improving the video quality of broadband IPTV services, Raptor code has been adopted in various broadband IPTV systems. In this paper, we propose a systematic Raptor code decoder based on the group parameters for a group of encoding symbols. For a Raptor code application that can frequently use one or several fixed block lengths (i.e., the number of source symbols in a source block) such as IPTV, we could produce the corresponding group parameters in advance and then the proposed decoder can use them to decode the received encoding symbols more efficiently. For the IPTV delivery scenario over a communication cloud based on DSL (Digital Subscriber Line) access networks, the simulation results show that our decoder is faster than the conventional Raptor code decoder which is adopted by DVB and 3GPP specifications.