[en] The Large High Altitude Air Shower Observatory (LHAASO) project consists of a complex detector array with over 6000 detector nodes spreading over 1.2 km² areas. The arrival times of shower particles are captured by time-to-digital converters (TDCs) in the detectors' frontend electronics, the arrival direction of the high energy cosmic ray are then to be reconstructed from the space-time information of all detector nodes. To guarantee the angular resolution of 0.5°, a time synchronization of 500 ps (RMS) accuracy and 100 ps precision must be achieved among all TDC nodes. A technology enhancing Gigabit Ethernet, called the White Rabbit (WR), has shown the capability of delivering sub-nanosecond accuracy and picoseconds precision of synchronization over the standard data packet transfer. In this paper we demonstrate a distributed TDC prototype system combining the FPGA based TDC and the WR technology. With the time synchronization and data transfer services from a compact WR node, separate FPGA-TDC nodes can be combined to provide uniform time measurement information for correlated events. The design detail and test performance will be described in the paper