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For orthogonal frequency-division multiplexing (OFDM) systems, the frequency offsets in mobile radio channels distort the orthogonality between sub-carriers that results in intercarrier interference (ICI). We combine turbo product code (TPC) with ICI self cancellation to counteract noise and ICI of the OFDM system over a fast fading channel. High-level quadrature amplitude modulation (QAM) is used to compensate for the bandwidth efficiency lost by TPC and ICI. Furthermore, an existing adaptive ICI self-cancellation scheme is improved by including TPC and high-level QAM. The basic concept and the structure of the improved adaptive scheme are introduced. The channel type and the signal-to-noise power ratio (SNR) are given as the metrics for adaptive switching among the selected candidates. Under the constraint of a target bit error rate (BER) of 10-6, the switching thresholds of SNR are determined and an adaptive strategy based on threshold switching is presented. Compared with existing schemes, the proposed adaptive scheme has higher average bandwidth efficiency, wider dynamic range of SNR, and stronger capability to combat the frequency offset at the target BER.