High-frequency (HF) radio communication has been recognized as the primary means for long-range wireless communications since the advent of radio. With its unique features, HF communication continues to be used for a wide range of civilian, government and military applications as a powerful alternative to a myriad of more sophisticated communication systems. However demanding requirements of high-speed data communications impose new requirements on the HF system design and innovative approaches are required. In this paper, building upon the promising concept of cooperative transmission, we investigate the performance of a multicarrier coded HF system with amplify-and-forward relaying. Specifically, we consider orthogonal frequency division multiplexing (OFDM) with bit-interleaved coded modulation (BICM) and demonstrate the achievable diversity through the derivation of pairwise error probability. We also conduct Monte Carlo simulations to confirm the analytical derivations and present performance comparisons.