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Ambient backscatter communication (AmBC) over orthogonal-frequency-division-multiplexing (OFDM) signals has recently been proposed as an appealing technique for low power Internet-of-Things (IoT) applications. The special spectrum structure of OFDM signals provides a range of flexibility in terms of bit-error-rate (BER) performance, data rate, and power consumption. In this paper, we study subcarrier-wise backscatter communication over ambient OFDM signals. This new AmBC is to exploit the special spectrum structure of OFDM to transmit data over its squeezed orthogonal subcarriers. We propose a basis transmission scheme and its two modifications to support a higher data rate with superior BER performance compared to existing methods. The basis scheme can transmit one bit per subcarrier using on-off keying (OOK) modulation in the frequency domain. In the first modification, interleaved subcarrier block transmission model is employed to improve the BER performance of the system in frequency-selective channels. It results in a trade-off between the size of the blocks and data rate. Thus, in the second modification, interleaved index modulation (IM) is employed to mitigate the data rate decrementation of the former modification. It also stabilizes and controls the power of the signal to result in interference reduction for a legacy receiver. Analytical and numerical evaluations provide a proof to see the performance of the proposed method in terms of BER, data rate, and interference.