I. Introduction
Over the last few decades, coherent detection combined with high-level modulation formats and advanced digital signal processing (DSP) has promoted the capacity increase in the optical fiber communication systems significantly. However, there still exist a few decibels in optical signal-to-noise ratio (OSNR) between the capacity of optical fiber communication systems and the Shannon limit [1]. In recent years, probabilistically shaped MQAM have been widely investigated to improve the performance and the flexibility of optical fiber communication systems. By assigning different probabilities to the constellation symbols, the probabilistically shaped MQAM allows both to dynamically adapt the information rate according to the link condition and to narrow the gap to the Shannon limit [2]–[4]. To correctly recover PS-MQAM signals at the receiver, some key DSP algorithms need to take the SD as a priori information. Such as, the inverse distribution matcher [5] and forward error correction (FEC) decoder [6]. Additionally, some studies have shown that the performance of frequency offset estimation, carrier phase recovery and polarization demultiplexing algorithms for PS-MQAM signal can be optimized according to SD [7], [8]. Consequently, the automatic SDI technique might take a very key role in the DSP blocks of the PS-MQAM signal receiver.