基于全局距离最优的抗污染极短纠错码设计

针对现有二维码在复杂环境中抗污染能力弱、解码速度慢的问题，提出了一种基于全局距离最优的抗污染极短纠错码。首先，构建了表征污染环境的凹凸多边形数学模型；然后，设计了采用3个编码点表示一个目标数据位的极短纠错码；最后，设计了在有限约束域内全局距离最优的编码点的编排方法，并给出了对应的解码算法。对极短纠错码的抗污染能力和识别速度进行了仿真评估，并与经典的BCH码进行了对比。结果表明，当目标数据长度为18、编码点数为63时，极短纠错码在同等污染环境中识别准确率接近BCH码，而解码速度是BCH码的130倍。所提编码还具有结构简洁明确、编码点数适应能力强、易于标准化推广应用等显著优点。

Design of very short antipollution error correcting code based on global distance optimization

The existing two-dimensional codes have the problems of weak antipollution ability and slow decoding speed in complex environment. To solve these problems， a very short antipollution error correcting code based on global distance optimization was proposed. Firstly， a concave-convex polygon mathematical model was constructed to characterize the polluted environment. Then， a very short error correcting code was designed， which uses three coding points to represent one target data bit. Finally， a coding point arrangement method was designed， which optimizes the global distance within a limited constrained domain. The corresponding decoding algorithm was also given. The antipollution ability and recognition speed of very short error correcting code were simulated and analyzed， and the proposed code was compared with the classical Bose-Chaudhuri-Hocquenghem （BCH） codes. The results show that when the target data length is 18 and the number of coding points is 63， the recognition accuracy of very short error correcting code is close to that of BCH codes in the same polluted environment with the decoding speed of 130 times of that of BCH codes. The proposed code also has the obvious advantages of simple and clear structure， strong adaptability of coding points， and being easy to be standardized and popularized.