Some Efficient Error Control Codes Designs for Various Error Channel Models

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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.