Abstract: As a new modulation method，high-dimensional modulation solves the contradiction between spectral efficiency and power efficiency． However， the high complexity of lattice coding and decoding result in transmission delay，which seriously affects the application of high-dimensional modulation technology in highspeed and high-capacity optical communication systems． To solve this problem， a low complexity high dimensional lattice coding and decoding method based on tree structure is proposed． The tree structure is constructed according to the lattice distribution law，and the lattice coding and decoding is finished by the tree
structure index algorithm． This method can effectively realize high-dimensional lattice coding and decoding．When the SNＲ is 16 dB，the bit error rate can reach 3． 1 × 10 － 4，and the complexity of lattice coding and decoding with points of M can be reduced from O( M) to O( log M) ，and is universal．

Key words: tree structure, high-dimensional modulation, lattice coding, lattice decoding