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An M-FSK modulation and time-diversity permutation coding scheme for narrow-band power-line communications combined with the soft-decision technique is investigated in this paper. A process to identify the errors caused by impulse noise and narrow-band interference, and to mitigate the error effects is proposed. We further present a permutation decoding algorithm and a majority-logic decoding process to correct the remaining additive errors. Due to its simplicity and low encoding/decoding complexities, this scheme therefore can be suitable for a simple but robust narrow-band power-line communications system of practical interest.