Topics in Pseudonoise Sequence Design and Error-Correcting Codes

伪噪声序列设计和纠错码主题

• 批准号: 0073555
• 负责人: P. Vijay Kumar
• 金额: $ 30万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-09-01 至 2004-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0073555&HistoricalAwards=false
• 关键词: Topics; Pseudonoise; Sequence; Design; Error

In this project, algebraic techniques are in use two to tackle two classes of problems related to improving the throughput and/orreliability of a communication link are under study. The first classof problems under study is the design of long and efficienterror-correcting codes. Such codes are of interest as longererror-correcting codes tend to ``average'' out the noise and henceprovide better performance. The second class of problems relatesto the design and analysis of families of signature sequences that areused to distinguish between the signals of different users in amulti-user environment. Examples of multi-user environments includeCode Division Multiple Access (CDMA) cellular and personalcommunication systems. More details on example problems drawn fromeach class are provided below. Since the early 80's, the promise of algebraic geometric (AG) codeshas been the delivery of a sequence of error-correcting codes ofincreasing length whose asymptotic performance exceeds theGilbert-Varshamov bound and for which efficient and practical encoding and decoding algorithms are available. Computationallyefficient decoding algorithms for AG codes are now available and therenow exist explicit descriptions of algebraic curves of the typerequired to construct these long codes. Construction of good codes on these curves requires the determination of a basis for a certain typeof vector space of functions defined on these curves. Theinvestigators study efficient methods of generating such bases. Theuse of novel algebraic geometry techniques to generate pseudo-randomsequences is an example of the type of problem belonging to the secondclass. The investigators examine methods of generating sequenceshaving pseudo-random properties such as low correlation and largelinear span. Also under investigation are more efficient means ofassessing the performance of pseudo-random sequences in a multi-usersetting, for example, more efficient means of determining the minimumEuclidean distance between adjacent multi-user signals. Theperformance in a multi-user setting, of a a specific sequence family,known as family S(2) and previously co-designed by the PI is alsounder study.

在这个项目中，正在使用两种代数技术来解决与改善通信链接的吞吐量和/遵守性有关的两类问题。 研究的第一类问题是设计长时间有效的校正代码。 此类代码引起了人们的关注，因为更长的校正代码倾向于``平均''消除噪声，因此可以更好地表现性能。 第二类问题相关的签名序列家族的设计和分析旨在区分Amulti-user环境中不同用户的信号。 多用户环境的示例包括eCode Division多访问（CDMA）蜂窝和个人通信系统。 下面提供了有关示例问题的更多详细信息。 自80年代初以来，代数几何（Ag）代数的承诺是提供一系列误差校正的increasing长度的代码，其渐近性能超过了吉尔伯特·瓦尔沙莫夫（Garshamov）的束缚，并且可以提供有效的，实用的编码和解码算法。 现在可以使用针对AG代码的计算效率解码算法，并且存在TherEnow的明确描述，这些代数曲线的代数曲线是构造这些长代码的类型曲线。 在这些曲线上构建良好的代码需要确定这些曲线上定义的功能的某些类型向量空间的基础。 评估者研究产生此类基础的有效方法。 新型代数几何技术生成伪随机序列的用途是属于第二阶段的问题类型的一个例子。 研究人员检查了生成测序避免伪随机特性的方法，例如低相关性和囊范围。 同样，在多个用户术中，研究中的伪随机序列的性能是更有效的方法，例如，确定相邻多用户信号之间的微型核糖距离的更有效方法。 特定序列家族（称为family S（2）和以前由PI共同设计的特定序列家族）的多用户中的性能是Alsounder的研究。