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OFDM is the digital modulation scheme that multiplexes multiple orthogonal sub-carriers that are digitally modulated. One of the schemes that improve the performance of OFDM transmission is the sub-carrier adaptive modulation scheme. In order to perform sub-carrier adaptive modulation, it is necessary to transmit the allocation information of modulation schemes for each sub-carrier and this degrades transmission rate. In order to improve this problem, the use of pre- coded OFDM is effective and it is possible to reduce amount of allocation information of modulation. In this paper, the scheme that controls the symbol modulation scheme, transmission power of each sub-carrier and coding rate according to the channel situation under the impulsive multi-path channel is analyzed in order to improve the performance of the adaptive modulation scheme of the pre-coded OFDM transmission.