A cycle elimination algorithm for construction of LT codes

Fountain codes which have been utilized extensively in deep-space communication can solve the problems, such as the asymmetry between the uplink and downlink, the enormous time delay and long distance. LT codes are the first codes fully realizing the digital fountain concept. The girth of the generator matrix is a key element, and short cycles in the generator matrix cause the degeneration of performance of LT codes. This paper proposed a PEG algorithm to construct the generator matrix can eliminate short cycles and also average the degrees of information nodes. The coding-performance can be greatly improved and the decoding-complexity decreased.