Some Efficient Error Control Codes Designs for Various Error Channel Models

针对各种差错信道模型的一些有效的差错控制码设计摘要在过去的五十年中，差错控制码被成功地用于提高现代计算机、通信和多媒体系统的可靠性。随着这些系统的数据率不断增加，以及许多应用需要更可靠、更安全的系统，预计需要设计更强大和更高效的代码来应用于这些系统。针对不同的差错模型，设计了几种有效的差错控制码。首先，研究了几种无差错反馈的Z信道容量实现码。在Z通道模型中，数据字中的错误仅为1到0类型。其次，在此基础上研究了几种新颖的分集合并ARQ(Automatic Repeat Request)协议。此外，还发展了与初等对称函数有关的一些理论。基于这一理论，设计了几类能够纠正t11到0和t0 0到1错误的新码类。此外，基于基本对称函数理论，研究了t-非对称纠错码、BCH和Goppa码、纠错平衡码、高阶谱零码等多种码的有效译码算法。文中还探讨了该理论在其他领域的应用。

Some Efficient Error Control Codes Designs for Various Error Channel Models AbstractIn the last five decades error control codes have been successfully used to improve the reliability of modern computer, communication and multimedia systems. As the data rate of these systems keeps increasing and as more reliable and secure systems are required for many applications, it is expected that more powerful and efficient codes need to be designed and applied to these systems. This research involves in the design of some efficient error control codes for various error models.First, some Z-channel capacity achieving codes with error free feedback are investigated. In a Z-channel model, the errors in a data word are of 1 to 0 type only. Next, based on this theory some novel diversity combining ARQ (Automatic Repeat Request) protocols are studied. Furthermore, some theory related to elementary symmetric functions is developed. Based on this theory, some new classes of codes capable of correcting t_1 1 to 0 errors and t_0 0 to 1 errors are designed. In addition, based on the elementary symmetric function theory some efficient decoding algorithms for many classes of codes - t-asymmetric error correcting codes, BCH and Goppa codes, error correcting balanced codes, higher order spectral null codes, etc. are studied. Some applications of the theory developed here to other areas are also investigated.