In space optical communication systems, multipulse position modulation (MPPM) has garnered notable attention due to its advantages, including high reliability, spectral efficiency, strong anti-interference capabilities, and low power consumption. However, traditional MPPM constellation points are not integer powers of 2, following by a partial mapping of MPPM constellation points due to constellation redundancy. Existing research has explored constellation point selection strategies for MPPM and proposed methods such as the Blahut?Arimoto algorithm and compressed sensing to maximize the constrained channel capacity. However, no feasible schemes have been proposed for addressing nonstandard constellation points in MPPM. Based on the traditional MPPM system and many-to-one mapping in probabilistic shaping, we propose a many-to-one mapping MPPM (MTO-MPPM) system to mitigate constellation redundancy and enhance the information transmission rate of MPPM. In traditional MPPM systems, information transmission rates are improved primarily through two methods: by increasing coding efficiency via convolutional code deletion, which, however, does not alter the channel capacity of MPPM, or by reducing the order of MPPM, which, however, is constrained by the number of mapping bits. Therefore, we compare the transmission rate adjustment performance of the proposed MTO-MPPM system with traditional convolutional code deletion and variable-order MPPM rate adjustment to highlight the advantages of MTO-MPPM.

The performance of the MTO-MPPM system is analyzed based on the SCPPM system. By increasing the number of bit symbol groups, the MTO-MPPM system incorporates more constellation points compared to traditional MPPM. For instances exceeding the available constellation points in MPPM, bit symbol groups are mapped to the same constellation points, addressing the issue of constellation points not being integer powers of 2. To avoid excessive fuzzy bits introduced by many-to-one mapping, the MTO-MPPM system restricts each constellation point to mapping a maximum of two bit symbols, resulting in at most one blurred bit per constellation. We investigate various MTO-MPPM constellation mapping schemes, including Gray mapping, anti-Gray mapping, and natural mapping. To ensure optimal performance, we adhere to the principle that a larger Hamming distance between constellation points corresponds to a greater time slot distance. The decoding algorithm for the internal soft-input soft-output module of the MTO-MPPM system is derived using the Bahl?Cocke?Jelinek?Raviv algorithm. Finally, the complete MTO-MPPM system is implemented and validated through MATLAB simulations.

In the 2-6MPPM system, MTO-MPPM employs a constellation mapping scheme based on Gray mapping, which increases the information transmission rate by 33% compared to traditional MPPM (Fig. 5). Furthermore, when the signal photons required for each bit of information transmitted by MTO-MPPM is 0.7 dB less than that of conventional MPPM, the bit error rate can achieve satisfactory performance. This improvement arises because Gray mapping aligns effectively with the principle that the greater the Hamming distance between constellation points, the larger the corresponding time slot distances. Simulation validations of the MTO-MPPM system were conducted for modulation orders of 7, 8, and 11. For an order of 7, the performance improvement of MTO-MPPM is modest. However, for orders of 8 and 11, the information transmission rate improves by 25% and 20%, respectively, with comprehensive performance gains of approximately 0.2 dB (Figs. 8 and 9). These results highlight that in MTO-MPPM systems, a smaller proportion of bits in many-to-one mapping leads to pronounced performance enhancements. A comparative analysis was conducted between MTO-MPPM and traditional methods for enhancing the information transmission rate, including adjusting MPPM order and modifying error correction code efficiency. When the modulation order of MTO-MPPM is 8, the overall performance improves by approximately 0.5 dB and 0.4 dB compared to reducing the order of traditional MPPM to 7 and lowering the bit rate via convolutional code deletion, respectively (Fig. 10). For an order of 11, the overall performance of MTO-MPPM improves by approximately 0.2 dB, 0.3 dB, and 0.4 dB relative to deleted 2-11MPPM, traditional 2-10MPPM, and traditional 2-9MPPM, respectively (Fig. 11). These results demonstrate that MTO-MPPM systems outperform traditional methods for modifying the information transmission rate through order adjustments or convolutional code deletion.

This study proposes an MTO-MPPM system to address constellation redundancy in traditional MPPM systems, where a subset of constellation points is often used for information transmission, and to optimize the information transmission rate. A novel constellation mapping scheme for MTO-MPPM is presented, and its decoding algorithm is derived. Simulation results demonstrate that in the MTO-MPPM system, smaller ratios of bits involved in many-to-one mapping yield pronounced performance enhancements. For modulation orders of 6, 8, and 11, the MTO-MPPM system achieves increases in the information transmission rate of approximately 33%, 25%, and 20%, respectively, while reducing the photons required for 1 bit transmission by 0.7 dB, 0.2 dB, and 0.2 dB, compared to traditional MPPM of the same order. In addition, compared to traditional MPPM systems that adjust the information transmission rate via variable order or convolutional code deletion, MTO-MPPM demonstrates better comprehensive performance.