An Adaptive Cycle Decrease Encoding Scheme for Short Length LT Codes

This paper proposes a novel cycle decrease encoding (CDE) scheme for short length LT codes over binary additive white gaussian (BIAWGN) channels. Two thresholds are introduced, which are used to decrease the number of cycles of length 4 in LT codes generator matrix. During the encoding process, information nodes whose number of cycles exceeding the threshold are screened continuously, and consequently the probabilities of their participation in latter encoding process are decreased and the degree distribution used by these information nodes are changed. The upper bound and lower bound of the number of cycles in any generator matrix are derived. The analysis is then used to calculate thresholds, enabling a sharp decrease of the number of cycles in generator matrix. Simulation results show that the short length CDE LT codes ($k= 50$ and 200) perform better than the conventional LT codes over BIAWGN channels.