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Here, the Jacobi iterative algorithm is applied to combat intersymbol interference (ISI) caused by frequency-selective channels. The performance bound of the equaliser is analysed in order to gain an insight into its asymptotic behaviour. Because of the error propagation problem, the potential of this algorithm is not reached in an uncoded system. However, its extension to a coded system with the application of the turbo-processing principle results in a new turbo equalisation algorithm, which demonstrates comparable performance with reduced complexity compared with some existing filter-based turbo equalisation schemes; and superior performance compared with some frequency domain solutions, such as orthogonal frequency division multiplexing and single-carrier frequency domain equalisation.