Some Efficient Error Control Codes Designs for Various Error Channel Models

针对各种错误通道模型的一些有效错误控制码设计 摘要 在过去的五年中，错误控制码已成功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以及许多应用需要更可靠和安全的系统，预计需要设计更强大和更高效的代码并将其应用于这些系统。本研究涉及针对各种错误模型设计一些有效的错误控制代码。首先，研究了一些具有无错误反馈的Z通道容量实现代码。在 Z 通道模型中，数据字中的错误仅为 1 到 0 类型。接下来，基于该理论，研究了一些新颖的分集结合ARQ（自动重复请求）协议。此外，还发展了一些与初等对称函数相关的理论。基于该理论，设计了一些能够纠正t_1 1到0错误和t_0 0到1错误的新型代码。此外，基于初等对称函数理论，研究了t-非对称纠错码、BCH和Goppa码、纠错平衡码、高阶谱空码等多类码的高效译码算法。还研究了这里开发的理论在其他领域的一些应用。

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.