###### Abstract  
As a typical high-order modulation format optimization technology, constellation probability shaping enhances generalized mutual information (GMI) by optimizing the probability distribution of each constellation point of the signal. It can improve the transmission capacity of the same order M Quadrature Amplitude Modulation (QAM) signal under the condition of limited average transmission power, and further narrow the gap with the Shannon limit capacity. The distribution matcher is a key part of constellation probability shaping since it not only ensures the one-to-one mapping of input and output sequences but also realizes the function of probability shaping. The constant composition distribution matcher (CCDM) structure is a widely utilized distribution matcher in the current probability shaping technology. Based on CCDM, a parallel distribution matcher scheme is proposed in this paper. It has a lower rate loss than CCDM for short output lengths (n is less than 100). Block lengths can be reduced by up to 30% with the same rate loss. When the GMI is the same as for the probability shaping (PS) 64 QAM signal using CCDM, the OSNR required by the PS-64 QAM signal using this scheme can be enhanced by 0.12 dB, the block length can be reduced by 40%, and the transmission distance in a standard single-mode fiber can be slightly extended. probabilistic amplitude shaping; constant composition distribution matcher; higher order modulation format signal; constellation shaping; LDPC coding +
Footnote †: journal: _Photonics_  
different symbols varies. As a result, it is compatible with the existing modulation receiving system and digital signal processing technology, and can be flexibly combined with a range of multiplexing methods and channel coding technology, with low system complexity [3], this paper focuses on constellation probability shaping. When the source obeys the continuous Gaussian distribution, the largest capacity can be achieved in the AWGN channel with power constraint P, according to [PERSON] [4]. For the probability shaping technology, the constellation points are dispersed discretely, making it difficult to determine what kind of distribution to use to approach the continuous Gaussian distribution. [PERSON] demonstrated in 1993 that the Maxwell-Boltzmann (MB) distribution is the optimum for constellation probability shaping [5]. Subsequently, many probability shaping schemes, such as Gallager's Scheme [6; 7; 8], Trellis Shaping [9], Concatenated Shaping [10], and Bootstrap Scheme [11], have been proposed to realize the shaping and optimization of QAM signals. [PERSON] and [PERSON] innovatively proposed a probabilistic amplitude shaping (PAS) architecture in 2015 that combined a constant-composition distribution-matcher (CCDM) with forward error correction (FEC) encoding to implement PS [12]. Coding and shaping are decoupled in the PAS scheme thanks to a parallel transmitter design, which substantially simplifies the implementation of encoder and decoder and makes PS techniques practical. Many researchers have proven that probability shaping technology improves transmission distance, spectrum efficiency, and bit error performance in communication systems using the PAS scheme [13; 14; 15; 16; 17; 18]. In the present high-order QAM modulation system, it is one of the preferred technologies. The distribution matcher is a key component of PAS since it not only ensures the one-to-one mapping of input and output sequences but also realizes the function of probability shaping. The CCDM structure [19] is a widely utilized distribution matcher in the current probability shaping technology. It is based on arithmetic encoding, and the rate loss of CCDM can only tend to zero as the output symbol length approaches infinity. Hardware implementation is relatively complex in today's high-speed optical communication system, and the complexity increases linearly with the length of symbols. Furthermore, arithmetic coding is a highly serial coding method.