## 5 Conclusions and Discussion  
As a key part of probability shaping technology, the distribution matcher has significant importance and application value for research. At present, the widely used constant composition distribution matcher is a progressive optimization scheme. It is only when the length of the output symbols is infinity long that the rate loss of CCDM is zero. In addition, it adopts arithmetic coding, which is a highly serial coding method. It represents the input and output sequences, respectively, by dividing intervals between intervals. When the number of input and output sequences is large, the intervals to be divided become greater and the boundary between intervals becomes blurred, which is difficult to distinguish and easy to make mistakes when mapping. Therefore, it is necessary to propose a distribution matcher structure with good performance under short block length. In this paper, we have proposed a novel parallel architecture distribution matcher, which is an improvement over conventional CCDM at short output block lengths. The output sequence has various compositions compared with the constant composition of the CCDM because of the parallel structure and pairwise optimization of the two CCDMs. As a result, the proposed structure has a lower rate loss when the output block lengths (n is less than 100) are the same and the output block lengths can be lowered by up to 30% with the same rate loss. In the simulation of an optical communication system of PS-64 QAM signal, compared with a CCDM signal with the same generalized mutual information, the PS-64 QAM signal employing this structure requires a lower OSNR, the block length can be reduced by 40%, and the transmission distance is increased. In detail, When GMI is 4 bit/symbol, compared with the uniformly distributed 64 QAM signal, the OSNR of the PS-64 QAM signal using CCDM is reduced by 0.35 dB, and the OSNR of the PS-64 QAM signal using the parallel distribution matcher is reduced by 0.47 dB, which is a 0.12 dB improvement. The improvement in transmission distance is small, and it is expected to further improve the transmission distance in combination with digital signal processing technology, which will be our future research direction. Other parallel distribution matcher schemes, such as parallel-amplitude distribution matcher [24], realize the function of symbol-level DM through multiple-bit-level DM. Therefore, M-1 bit-level DM is required to map sequences with M output amplitude values. For high-order QAM format, the number of bit-level DM required increases with the increase in modulation order, and the overall structure of the system is complex. In addition, the multiset-partition distribution [20], which also adopts the idea of pairwise optimization, needs to build a Huffman tree structure to index different complementary pairs and uses serial processing for the input data. The coding process is complex and  
Figure 8: The BER performance over transmission distance in the standard single-mode fiber transmission link. The transmission distance of PS-64 QAM signals using the parallel distribution matcher is slightly larger than that of PS-64 QAM signals using CCDM. error-prone. In contrast, the scheme proposed in this paper is a two-stage parallel structure. No matter how high the order of the QAM signal is, only two CCDMs are required. At the same time, the input data are processed in the two CCDMs after serial-parallel conversion. The receiver performs a corresponding parallel-serial conversion. There is no complex coding process; so, the structure is simple. Conceptualization, Y.Z. ([PERSON]); methodology, Y.Z. ([PERSON]) and H.W. ; software and validation, Y.Z. ([PERSON]); writing--original draft preparation, Y.Z. ([PERSON]); supervision and project administration, H.W., Y.J. and Y.Z. ([PERSON]); funding acquisition, H.W., Y.J. and Y.Z. ([PERSON]). All authors have read and agreed to the published version of the manuscript. Not applicable.