基于叠加度的有限长系统LT码编码方案

Finite length systematic LT codes based on superposing degree distribution

提出了一种基于叠加度的系统卢比变换(Luby transform,LT)码编码方案。与需要预编码的系统Raptor码或交织编码的准系统掺杂LT码方案不同,由掺杂度分量与弱鲁棒孤波分布进行叠加的叠加度分布,使得系统LT码的中间节点能以LT编码方式构造输出节点。理论分析了优化掺杂度分量叠加比例的系统LT码具有译码渐近性能,对给定码长k和冗余开销ε的编译码复杂度为O(k·ln(1/ε))。仿真验证了优化后的有限长系统LT码克服了系统Raptor码在信道删除概率大于0.01即出现误码平台的问题,在译码失败概率10-4时相对于准系统掺杂LT码的所需译码冗余开销可降低12%~20%。

A novel superposing degree distribution （SPDD） is designed for systematic Luby transform （LT） codes. Compared with pre-coding systematic Raptor codes and interleaving encoding Quasi systematic doped LT codes （QS-DLT）, SPDD is designed based on weaken robust degree distribution superposing with a doping de- gree （DD） distribution, and the systematic-form output symbols are generated by the intermediate symbols with LT-encoding. By optimizing of the superposing proportion of DD, the asymptotic performance of systematic LT codes is analyzed, and the coding complexity is O（k ·ln（1/ε））, where k is the code length and ε is the overhead. Simulation results show that, the proposed systematic LT codes solve the error floor problem in the systematic Raptor codes when the channel erasure rate is larger than 0.01, and can achieve decoding failure rate of 10-4 with a 12%-20% reduction in overhead when compared to the QS-DLT codes.