On the Fly Belief Propagation Decoding Algorithm for LT Codes

As the first realisation of Fountain Codes, Luby Transform (LT) codes provide high reliability and scalability and low complexities for data transmission in networks. Two basic algorithms, Belief Propagation (BP) and Gaussian Elimination (GE), were introduced to decode LT codes. However, both of them execute their decoding process only after all the encoded symbols have been received by decoder, which results in the waste of time, storage space and computing resource. In this paper, an improved decoding algorithm termed on the fly belief propagation (OFBP) for LT codes is proposed. Based on the BP algorithm, OFBP performs the decoding processing once each encoded symbol arrives thus distributing the decoding work during all symbols reception. Compared with the traditional BP algorithm, the actual decoding time of the proposed algorithm is highly shortened. Moreover, without processing all the encoded symbols, the actual storage space and decoding complexity are greatly reduced while maintaining the same performance relative to the traditional BP decoding scheme.