In a multi-carrier (MC) system, the transmitted data are split across several sub-carriers as a crucial approach for achieving high data rates, reliability, and spectral efficiency. Deep learning (DL) enhances MC systems by improving signal representation, leading to more efficient data transmission and reduced bit error rates. In this paper, we propose an MC system supported by DL for operation on fading channels. Deep neural networks are utilized to model the modulation block, while a gated recurrent unit (GRU) network is used to model the demodulation blocks, acting as the encoder and decoder within an autoencoder (AE) architecture. The proposed scheme, known as MC-AE, differs from existing AE-based systems by directly processing channel state information and the received signal in a fully data-driven way, unlike traditional methods that rely on channel equalizers. This approach enables MC-AE to improve diversity and coding gains in fading channels by simultaneously optimizing the encoder and decoder. In this experiment, we evaluated the performance of the proposed model under both perfect and imperfect channel conditions and compared it with other models. Additionally, we assessed the performance of the MC-AE system against index modulation-based MC systems. The results demonstrate that the GRU-based MC-AE system outperforms the others.