现代通信中的离散结构问题

项目名称： 现代通信中的离散结构问题

项目编号： No.11271042

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 常彦勋

作者单位： 北京交通大学

项目金额： 60万元

中文摘要： 组合设计理论主要研究各种离散结构的存在性和构造问题，当代设计理论越来越注重研究具有重要实际应用的组合结构。本项目从现代通信的安全与效率出发，拟研究在其中具有重要应用的两类组合离散结构问题：(1)研究最优脉冲无线电序列的构造方法，并确定其所含码字的个数；注重脉冲无线电序列所要求的脉冲位置性，运用组合、代数和几何的工具寻找脉冲无线电序列所含码字个数（紧的）上界，并构造满足上界的最优脉冲无线电序列；探索与之密切相关的具有脉冲位置性的循环设计与循环填充设计的构造方法。（2）研究量子跳跃码与自发发射纠错设计之间的内在本质联系；刻画量子跳跃码的组合特性；研究自发发射纠错设计本身的构造方法及与其他相关组合设计的联系;研究其他类型量子纠错码，描述其组合特性，研究其存在性、构造方法和性质。

中文关键词： 离散结构；脉冲无线电序列；量子跳跃吗；自发发射纠错设计；组合编码

英文摘要： Combinatorial design theory, a branch of Discrete Mathematics, mainly studies existence and constructions of various combinatorial configurations. Modern design theory attaches more importance to the combinatorial structures which have intimate connections with current and practical applications. This project considers the safety and efficiency of modern communications and is mainly devoted to investigating two types of combinatorial configurations. Specifically, the research content is outlined as follows: (1) the construction methods of optimal impulse radio sequences (IRS) will be studied and the exact number of their codewords is expected to be determined; the impulse position property will be paid much attention and combinatorial, algebraic, and geometric tools will be combined to establish the upper bound of the number of codewords in an optimal IRS; the optimal IRS with some specified parameters will be constructed; the cyclic designs (or packings) with impulse position property, an intimate design with IRS, will be explored. (2) the intrinsic and essential connection between quantum jump codes and spontaneous emission error designs (SEED) will be researched; Combinatorial properties of quantum jump codes is expected to be characterized; the construction of SEED and related designs will also be investigat

英文关键词： combinatorial configuration；impulse radio sequence；quantum jump code；spontaneous emission error design；combinatorial code