A STUDY OF SOME CODING PROBLEMS AND ERROR CONTROL TECHNIQUESFOR DATA COMMUNICATIONS

本研究课题探讨了编码理论中应用于可靠数据通信的几个基本问题。主要研究领域有：(1)具有多级纠错能力的码；(2)线性分组码的权重分布；(3)分组编码调制；(4)用于错误控制的编码技术。在第一个区域中，寻找能够为消息的不同部分提供不同级别的错误保护的代码。应用的一个例子是广播频道，其中不同的接收器在不同的噪声环境中工作，因此需要不同级别的保护。第二个研究领域的动机是需要更简单的方案来评估更广泛类别的代码的错误控制性能。第三个领域解决了组合调制和分组编码的问题，以实现高可靠和带宽高效的数据通信系统。类似的技术，但使用网格（或卷积）编码而不是块编码，已经成为现代数据系统（特别是语音波段和卫星频道）的重要应用。最后一个领域是级联编码思想的持续发展，它是串联编码的概括。这个概念与前面的主题相结合，可以引导开发具有极低错误概率的系统，并且分配的信道带宽增加最少。除了对当前的数据传输问题提出具体的解决方案外，该项目很可能为未来的编码理论研究奠定基础。

This research topic investigates several fundamental topics in coding theory as applied to reliable data communication. The major areas of study are: (1) codes with multi-level error- correcting capabilities, (2) weight distributions of linear block codes, (3) block coded modulation, and (4) coding techniques for error control. In the first area, codes are sought which can provide different levels of error protection for different parts of a message. An example of application is the broadcast channel where different receivers operate in different noise environments, hence requiring different levels of protection. The second research area is motivated by the need for simpler schemes to evaluate the error control performance of broader classes of codes. The third area addresses the problem of combined modulation and block coding to achieve highly reliable and bandwidth-efficient data communication systems. Similar techniques, but using trellis ( or convolutional) coding rather than block coding, have emerged as an important application in modern data systems ( especially for voice-band and satellite channels). The final area is the continued development of the idea of cascaded coding, which is a generalization of concatenated coding. This concept, in conjunction with the preceding topic, could lead the way to development of systems with extremely low error probability with a minimal increase in assigned channel bandwidth. In addition to suggesting specific solutions to current data transmission problems, this project is likely to lay the groundwork for future research in coding theory.