| A relatively new model of error control is the limited magnitude error over high radix channels. In this error model, the error magnitude does not exceed a certain limit known beforehand. In this dissertation, we study systematic error control codes for common channels under the assumption that the maximum error magnitude is known a priori. Optimal codes correcting all asymmetric and symmetric errors are given. Further, as it is often the case that we only need to correct a small number of errors, codes that can correct a single error over asymmetric and symmetric channels are also proposed. The designed codes achieve higher code rates than single error correcting codes previously given in the literature. From the error detection point of view, we study both all and t error detecting codes for asymmetric/unidirectional channels and design close-to-optimal codes. Finally, we show how the all asymmetric error correcting codes proposed in this dissertation can be used to detect all symmetric errors. |
