Multi-Carrier Modulation (MCM) is one of the most interesting data transmission technologies over the copper wire in high-performance communication networks. The most modern data transmission systems that efficiently implement the MCM techniques in the real world applications and reach very interesting and reliable results are the Digital Subscriber Line (DSL) technologies. The efficient types of MCM modulation schemes, such as Carrierless Amplitude/Phase (CAP) and Discrete-Multitone (DMT), which increase the bandwidth efficiency and the connection security so this will help the (ADSL) to operates data rate more than 6 Mbit/s downstream and 640 Kbit/s upstream with relatively error free transmission over twisted copper wires. In this work, the probability of error of the two coding methods DMT and CAP are rurally showed the difference between these two methods where the maximum probability of error reach to 0.7*10 _1 when the SNR equal to 0dB and minimum probability of error is 10 _3 when the SNR is 38dB. The simulated multicarrier system (DMT, CAP) and they are performances were examined under different channel impairments including Additive White Gaussian Noise AWGN channel conditions in the ADSL environment. The error correction coding technique, Reed-Solomon coding was used in the system in order to ensure the high error-correction capabilities during data transfer over the noise-impaired physical channels, and it was also simulated in the frequency domain. The general computer program simulates the coding techniques in the ADSL transceiver system and the program tests show that the simulations of the ADSL in combination with the two modulation schemes DMT and CAP under various channel impairments like AWGN and near end crosstalk NEXT.