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This paper presents a general analysis of the achievable diversity and coding gains of orthogonal frequency-division multiplexing systems using linear constellation precoding and subcarrier grouping over multipath fading channels. It shows that the maximum diversity gain can be achieved with any subcarrier grouping scheme, as long as its group size F is not less than the number of effective resolvable paths L. For F ges L, the maximum coding gain can be achieved if F is an Euler number or an integer power of 2. Otherwise, the achievable coding gain approaches at least 70% of the maximum one. The analysis also proves the existence of a unique solution for optimum subcarrier grouping to achieve the maximum coding gain when F = L. Simulation results support the analytical prediction on the diversity and coding gains.