## 1 Introduction  
Because of its dependability and efficiency, many standards organizations have acknowledged and embraced multi-carrier (MC) transmission [1] for wireline and wireless systems [2, 3]. Key advantages of this method include its enhanced capacity to reduce inter-symbol interference (ISI) and its resistance to single-frequency interference. MC is a popular choice for emerging applications such as wireless local area networks (WLANs) [4] and power line communications (PLC) [5] thanks to its capacity to withstand a range of channel impairments, including impulse noise and frequency selectivity. The fundamental idea behind the MC protocol is to use complex exponentials as information carriers to break the spectrum down into a number of orthogonal narrowband subchannels [6]. The two most frequently used MC techniques are discrete multi-tone (DMT) [7] for wireline systems and orthogonal frequency-division multiplexing (OFDM) [8], which is mostly utilized in wireless applications. Recently, numerous advanced multi-carrier (MC) techniques based on OFDM have been explored to provide enhanced energy and spectrum [9; 10]. Among these, OFDM employing index modulation (OFDM-IM) stands out as a promising approach. OFDM-IM is a viable alternative for next-generation wireless communication that transmits data more efficiently than conventional OFDM. Index modulation (IM) encodes information not only in data symbols but also in the indices of active elements, enabling additional data transmission without requiring extra bandwidth [11]. This technique enhances data throughput as well as resilience against frequency-selective fading and interference by leveraging diverse subcarriers and indices. Moreover, the selective activation of subcarriers supports energy-efficient operation, making it suitable for energy-conscious applications [12]. The ability of OFDM-IM to mitigate both inter-symbol and inter-carrier interference while balancing spectral efficiency, energy efficiency, and system complexity makes it a versatile choice for modern wireless networks [13]. Several works have been conducted on OFDM-IM [14; 15]. In [16], a noncoherent OFDM-IM system based on maximum likelihood (ML) was proposed where the information bits were transmitted solely through the indices of active subcarriers. Low-complexity near-optimal detectors for OFDM-IM were introduced in [11] to address the computational challenges of ML detection, which is intensive due to the presence of index bits. The log-likelihood ratio (LLR) detector was introduced in [17]. Although it achieves near-ML performance, knowledge of the incoming signal's noise power spectral density is required, which represents a drawback. A low-complexity OFDM-IM detector that encodes every potential subcarrier activation pattern (SAP) was presented in [18]. This approach overlooks the possibility of incorrect SAP detection by using every potential SAP to transmit data. In [19], a greedy detector (GD) based on energy detection was proposed to estimate OFDM-IM performance with significantly lower complexity, although it did not achieve near-optimal performance. Reliable data transmission in OFDM-IM relies on accurate detection, as it ensures proper decoding of both index and data symbols, an enhanced bit error rate (BER), resilience to channel impairments, and preservation of communication quality [20]. Deep learning (DL) excels in handling high-dimensional complex data, adapting to varying conditions, and performing end-to-end optimization, making it ideal for efficient signal detection and data processing in communication systems [21; 22; 23]. Thus, DL may serve as a promising approach for OFDM-IM systems. Various DL-based strategies have been explored to simplify OFDM-IM implementations while achieving near-optimal performance [24; 25; 26]. A deep neural network (DNN)-based OFDM-IM system called DeepIM was proposed in [27]. The authors investigated the performance of the proposed model by utilizing both rectified linear units (ReLU) and hyperbolic tangent (Tanh) activation functions.