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[1]. 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[2]. 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.