正则低密度纠删码的分析

Analysis of regular low-density erasure codes

深入研究了基于正则度序列的低密度纠删码,通过对正则度序列的详细分析,提出了正则低密度纠删码可接受最大损失的一个结论.利用这一结论对(3,6)和(d,nd) 正则度分布给出了两阈值δ (3,6)与δ (d,nd)的关系(d≥3,n≥2).同时从理论上证明了基于(d,2d) 正则度序列的低密度纠删码都不是渐近最优码(d≥3),而且给出了这一结论的直观性解释和仿真结果.这些分析有助于低密度纠删码度序列的设计.

A detailed study of low-density erasure codes based on regular sequences of degree distribution is made. By analyzing regular sequences of degree distribution in detail a result is presented on the maximum tolerable loss fraction for regular low-density erasure codes. By using this result the relationship of two thresholds δ* (3, 6) and δ* (d, nd) is given for (3,6) and (d, nd)-regular degree distributions (d≥3, n≥2). In the meantime, it is shown that low-density erasure codes based on (d, 2d)-regular sequences of degree distribution are not close to optimum from the theoretical point of view of theory. Moreover, the simulation and intuition are given as to why regular codes are not close to optimum. These analyses will be helpful in designing the sequences of degree distribution for low-density erasure codes.