中文摘要：

有限平面LDPC码是一类重要的有结构的LDPC码，在利用和积算法（SPA）等迭代译码方法进行译码时表现出卓越的纠错性能。众所周知，次优的迭代译码不是最大似然译码，因而如何对迭代译码的性能进行理论分析一直是LDPC码的核心问题之一。近几年来，Tanner图上的停止集（stopping set）和停止距离（stopping distance）由于其在迭代译码性能分析中的重要作用而引起人们的重视。该文通过分析有限平面LDPC码的停止集和停止距离，从理论上证明了有限平面LDPC码的最小停止集一定是最小重量码字的支撑，从而对有限平面LDPC码在迭代译码下的良好性能给出了理论解释。

英文摘要：

Finite plane LDPC codes are important structured LDPC codes, which have excellent performance under iterative decoding algorithm. It is a key problem that to evaluate the performance of LDPC codes under iterative decoding. Recently, the stopping sets and stopping distance of Tanner graph are of interests in performance evaluation. In this paper, the smallest sets of finite plane LDPC codes are studied. It shows that for finite plane LDPC codes, a smallest stopping set is the support of a codeword. These results give positive consequences for the good performance of finite plane LDPC codes under iterative decoding.