## 1 Introduction  
Visible light communication (VLC) is a promising alternative for complementing the overcrowded radio frequency bandwidth of wireless communication owing to its license-free operations, relative low cost, high spatial diversity, high bandwidth efficiency, and electromagnetic interference-free transmission [1, 2, 3, 4, 5, 6, 7]. Orthogonal frequency division multiplexing (OFDM) has been extensively used in VLC to maintain a better transmission rate due to its high spectral efficiency and low-complexity implementation to achieve better transmission rates [8, 9]. Recently, the combination of multiple-input multiple-output (MIMO) and index modulation [10, 11, 12, 13] to convey additional bits has gained a lot of attention in VLC literature. There are several published papers that investigated different aspects of the index modulation technique, such as non-coherent detection [14], low complexity detection [15], or precoding [16]. In addition, index modulation was proposed in optical communication [17] and later in [18] to implement generalized \(4\times 4\) light-emitting diode (LED) index modulation (GLIM-OFDM); in which the four transmitter side LEDs were divided into groups to transmit real-imaginary and positive-negative signals separately. As a result, depending on every OFDM symbol, just one LED in each group was chosen to convey the OFDM symbol parts. In [19], an LED selection algorithm for GLIM-OFDM was introduced to determine the best active LED combination to improve the system performance. In general, a maximum likelihood (ML) detector is cost-ineffective and unpractical for an OFDM-based communication system. According to [18, 19], maximum a posteriori (MAP) detectors are better than zero-forcing (ZF) and minimum mean square error (MMSE)detectors because of their better bit error rate (BER) performance and reasonable demodulation complexity. However, because all previously mentioned detectors only consider the instantaneous signal received at the receiver, the underlying relationship between the generated OFDM symbols is not fully exploited in the demodulation process. Deep learning (DL) has had an enormous impact on various research fields over the last couple of years; it has been applied in wireless communication since then [20; 21; 22; 23]. Many researchers have already suggested DL solutions to wireless communication problems, e.g., modulation detection and signal detection [24]. VLC channel models, similar to radio frequency channel models, have been developed according to probability and signal processing theories. Furthermore, DL techniques have recently made a number of advancements in the VLC system. Since the VLC transmission must be able to support a variety of constraints, such as dimming and lighting, according to user preferences in practical applications, the implementation of DL becomes more challenging. In [25], a data-driven approach based on DL was proposed to predict the outage events in a line-of-sight link. In [23], DL-based constellation design scheme for MIMO-VLC systems was introduced, which can significantly reduce complexity compared to existing schemes while maintaining a near-optimal performance. Despite a wide range of promising applications, the performance of VLC systems has been impaired by the high SNR required to achieve a low error rate for a variety of scenarios. Therefore, DL approach can be applied to VLC systems to improve performances in practical high-speed and low error-rate indoor transmission application, such as hospital facility. To the best of the authors' knowledge, no researcher has used DL to improve the BER performance of the GLIM-OFDM system. In this paper, a deep neural network (DNN)-aided active LED index estimator (IE) for improving the GLIM-OFDM detector performance in the VLC system is proposed. Unlike traditional DNN-based detectors, which directly estimate the transmitted bits at the transmitter side, the proposed method extracts the feature of the active LED index set with the time-domain signal of the receiver.