Low-Density Parity-Check (LDPC) codes are among the best error correcting codes known and have been adopted by data transmission standards, such as DVB-S2 or WiMax.They are based on binary sparse parity check matrices and usually represented by Tanner graphs. LDPC decoders require very intensive message-passing algorithms, also known as belief propagation. This paper proposes a very compact stream-based data structure to represent such a bipartite Tanner graph, which supports both regular and irregular codes. This compact data structure not only reduces the memory required to represent the graph but also puts it in an appropriate format to gather data into streams. This representation also allows to map the irregular processing behavior of the Sum Product Algorithm (SPA) used in LDPC decoding into the stream-based computing model. Stream programs were developed for LDPC decoding and the results show significant speedups obtained either using general purpose processors, or graphics processing units. The simultaneous decoding of several codewords was performed using the SIMD capabilities of modern stream-based architectures available on recent processing units.