Low-Density Parity-Check (LDPC) codes belong to a class of linear block codes that can approach the Shannon limit. However, due to the high decoding complexity, LDPC codes with extremely long block lengths will result in large decoding latency in practical applications. Recently, Cloud Radio Access Networks (C-RANs) have attracted much attention because of their innovative architecture, which involves embedding cloud computing capability into wireless networks. In this context, C-RANs provide an ideal platform for breaking the decoding bottleneck of LDPC codes with extremely long block lengths. However, given that there are currently as yet no specific cloud computing techniques proposed for C-RAN, the data processing architecture for LDPC decoding is still an open problem. In this paper, based on the Spark cloud computing platform, a data processing architecture is proposed for realtime decoding of extremely long LDPC codes. Based on the principle behind the belief propagation (BP) decoding algorithm, a novel distributed BP decoding algorithm is proposed and implemented on a Spark based cloud computing platform. Extensive experimentation illustrates that the proposed architecture enjoys a significant performance gain in decoding latency. Therefore, this work can be seen as a promising example of applying powerful cloud computing techniques to enhance the performance of wireless networks.