Some Efficient Error Control Codes Designs for Various Error Channel Models

几种适用于不同信道模型的有效差错控制码设计 在过去的五十年里，差错控制码已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速率不断增加，并且随着许多应用需要更可靠和安全的系统，期望需要设计更强大和有效的代码并将其应用于这些系统。本研究针对不同的错误模型，设计出一些有效的错误控制码。首先，研究了几种具有无错误反馈的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。然后，基于该理论研究了几种新型的分集合并ARQ（自动重传请求）协议。进一步发展了与初等对称函数有关的一些理论。基于这一理论，设计了几类新的能纠正t_1 1 ~ 0错误和t_0 ~ 1错误的码。此外，基于初等对称函数理论，研究了t-非对称纠错码、BCH码和Goppa码、纠错平衡码、高阶谱空码等多种码的有效译码算法。一些应用的理论在这里开发到其他领域也进行了研究。

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.