The combination of probabilistic shaping (PS) technology and forward error correction (FEC) technology can significantly boost the performance of a transmission system. In this paper, we propose a probabilistic shaping distribution matching algorithm employing uneven segmentation for data center optical networks, while keeping extremely low computational complexity for both encoding and decoding. Based on the proposed probabilistic shaping distribution matching algorithm, we develop a novel integrated scheme of PS and FEC coding that lifts the restrictions on the use of FEC technology and increases the use of interleaver. An experiment used to evaluate the probabilistically shaped data transmission is successfully conducted over a 25 km standard single-mode fiber (SSMF) with 16 quadrature amplitude modulation (16-QAM). Simultaneously, we use a simulation software to analyze the bit error rate performance at higher resolution. The results show that the joint coding scheme can achieve a 0.4dB performance improvement compared with the single FEC system.