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In this article, modulation diversity (MD) for frequency-selective fading channels is proposed. The achievable performance with MD is analyzed and a simple design criterion for MD codes for Rayleigh-fading channels is deduced from an upper bound on the pairwise error probability (PEP) for single-symbol transmission. This design rule is similar to the well-known design rule for MD codes for flat fading and does not depend on the power-delay profile of the fading channel. Several examples for MD codes with prescribed properties are given and compared. Besides the computationally costly optimum receiver, efficient low-complexity linear equalization (LE) and decision-feedback equalization (DFE) schemes for MD codes are also introduced. Simulations for the widely accepted COST fading models show that performance gains of several decibels can be achieved by MD combined with LE or DFE at bit-error rates (BERs) of practical interest. In addition, MD also enables the suppression of cochannel interference.