Improved Short Length LT Codes for BIA WGN Channels

Abstract

While gaining increasing popularity, rateless codes, especially for short length Luby transform (LT) codes, are known to perform poorly over noisy channels. The decoding process of LT codes is analyzed, which shows that the low decoding success probability of short length LT codes is predominantly caused by lack of degree 1 check nodes (CNs). Based on this observation, a novel improved encoding scheme for short length LT codes over binary additive white gaussian noise (BIA WGN) channels is proposed. A new degree distribution and two weighting factors are presented, which are used to improve the proportion of degree 1 CNs. In addition, by setting a threshold, information nodes (INs) whose degrees are less than the threshold are screened continuously, and then extra degrees were added to these INs to improve the error floor performance of short length LT codes. Furthermore, the design principles of above parameters are presented, enabling the validity and universality of the improved scheme. Simulation results show that the improved short length LT code ($\pmb{k=50}$ and 200) can decrease the bit error rate (BER) by up to five orders of magnitude over BIAWGN channels.