Design and optimization of MIMO-GSM-VLC systems based on protograph LDPC codes

Weikai JIANG, Liang LÜ, Zhaojie YANG, Yi FANG

Journal of Tsinghua University(Science and Technology) ›› 2025, Vol. 65 ›› Issue (11) : 2112-2120.

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Journal of Tsinghua University(Science and Technology) ›› 2025, Vol. 65 ›› Issue (11) : 2112-2120. DOI: 10.16511/j.cnki.qhdxxb.2025.27.033
Frontiers in New-Quality Communication Technology

Design and optimization of MIMO-GSM-VLC systems based on protograph LDPC codes

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Abstract

Objective: Indoor visible light communication (VLC) suffers from the low modulation bandwidth of a single light-emitting diode (LED), which hardly meets the demand for high-rate transmission. As a multiple-input-multiple-output (MIMO) technology, generalized spatial modulation (GSM) allows indoor VLC systems to achieve high spectral efficiency and excellent anti-interference capability using multiple LEDs for data transmission. However, in indoor MIMO-GSM-VLC systems, narrow spacing between multiple LEDs makes the channel characteristics between different LEDs and photodetectors very similar, resulting in a high correlation of the channel matrix. Because of the special characteristics of the VLC channel, the existing constellation mapping and channel coding schemes are no longer feasible for indoor MIMO-GSM-VLC systems. Therefore, incorporating the spatial characteristics of the VLC channel to develop a high-reliability and high-efficiency optical transmission scheme is imperative. Methods: The proposed optical transmission scheme is divided into two parts: a constellation mapping scheme and an improved protograph low-density parity-check (LDPC) code. First, this paper proposes a novel spatial multipulse position modulation (MPPM) mapping scheme, called the unequal power spatial MPPM (UPSM) constellation, to realize the joint optimization of GSM and MPPM. In particular, owing to the correlation of the VLC channel matrix, effective LED activation groups with similar characteristics transmitting MPPM symbols will cause serious intergroup interference in the MIMO-GSM-VLC system. Based on the VLC channel matrix, the principle and calculation method of influence coefficients for LED activation groups are presented to reallocate the peak transmit power of the MPPM symbols for effective LED activation groups, which can efficiently mitigate the attenuation of MPPM symbols in transmission. In addition, the maximum Hamming distance principle is used to optimize the mapping relationship between MPPM labels and MPPM symbols in the UPSM constellation. Consequently, the proposed UPSM constellation can be constructed by power allocation and label-to-symbol mapping optimization. Second, this paper proposes an improved protograph LDPC code with the aid of a protograph extrinsic information transfer (PEXIT) algorithm and an asymptotic weight distribution (AWD) function. In particular, some empirical constraints (including matrix dimension and variable node degree distribution) are imposed on the protograph (i.e., the base matrix) to reduce the encoding and decoding complexity. Next, based on a computer search method, the PEXIT algorithm optimizes the protograph LDPC code to achieve the minimum decoding threshold, leading to substantial bit-error-rate (BER) performance in the low signal-to-noise ratio (SNR) region. Furthermore, to avoid the error floor in the high SNR region, the AWD function is employed during the construction of the improved protograph LDPC code, guaranteeing that the protograph enables the linear minimum distance growth property. Results: The simulation and analysis results show that the proposed UPSM constellation mapping scheme considerably outperforms the natural constellation, Gray-like label (GL) constellation, and unequal power GL (UPGL) constellation. In addition, the proposed improved protograph LDPC code exhibits excellent convergence performance and the lowest decoding threshold compared with the existing counterparts in the MIMO -GSM-VLC system with the proposed UPSM mapping scheme. Conclusions: This paper conducts an in-depth investigation of the joint design of protograph LDPC codes and spatial MPPM constellation. The proposed constellation mapping scheme and the improved protograph LDPC code benefit from the remarkable BER performance and strong antifading robustness. Given these advantages, the proposed schemes are expected to be competitive solutions for indoor VLC applications.

Key words

visible light communication / protograph low-density parity-check codes / generalized spatial modulation / spatial multipulse position modulation constellation mapping scheme

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Weikai JIANG , Liang LÜ , Zhaojie YANG , et al. Design and optimization of MIMO-GSM-VLC systems based on protograph LDPC codes[J]. Journal of Tsinghua University(Science and Technology). 2025, 65(11): 2112-2120 https://doi.org/10.16511/j.cnki.qhdxxb.2025.27.033

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