摘要： 在如今大数据和机器学习不断扩大的背景下，分布式计算系统成为处理庞大数据的必要工具。对于有一定规模的计算集群，其性能会不可避免的受到“系统噪声”的影响，故而考虑在分布式计算系统中借助编码技术来增强系统的鲁棒性。大多数现有应用于分布式矩阵计算的编码方案均为固定速率码，因而无法适应节点数量动态变化的实际情况。同时，由于部分任务有截止期限制，故而应在保证任务顺利完成的前提下尽可能的减少平均开销从而降低时延。针对该问题，提出将LT码应用于雾计算场景下的分布式矩阵计算。依托其无速率特性，可以自适应信道状态变化。通过合适的度分布函数设计以及双向切割、因子化度数的方法以达到降低时延、增强分布式计算系统鲁棒性的预期效果。实验结果表明，在k1值固定的前置条件下，与FLT码及BDC-LT算法相比，Remo2算法的 值相对于前者可以稳定降低33.3％，相对于后者减少了7.7％的冗余。此外，当k1k2大小的码长固定时，k1、k2的离散化程度越低，即 会带来更小的平均开销 。

Abstract: In the context of the continuous expansion of big data and machine learning, distributed computing systems become necessary tools for processing massive data. For computing clusters with a certain scale, their performance are inevitably be affected by "system noise". Therefore, it can be considered to enhance the robustness of the system in distributed computing systems using encoding technology. Previously, researchers proposed a series of encoding schemes for distributed matrix computing, but since these schemes are all fixed rate codes, they cannot adapt to the dynamic changes in the number of nodes. At the same time, due to deadline constraints on some tasks, it is necessary to minimize the average cost and latency while ensuring smooth completion of the tasks. To address this issue, it is proposed to apply LT code to distributed matrix computation in fog computing scenarios. Relying on its rate free characteristics, it can adapt to changes in channel state. Through appropriate Degree distribution function design, two-way cutting and factorization degree method, the expected effect of reducing delay and enhancing the robustness of distributed computing system is achieved. The experimental results show that under the front conditions of the k1 value, compared with the FLT code and BDC-LT algorithm, the value of the Remo2 algorithm can be stabilized by 33.3 % compared to the former and it reduces redundancy by 7.7% compared to the latter. When the size of the k1k2 size is fixed, the lower degree of discreteness of k1 and k2, that is, will bring smaller average expenses.