Coherent optical communication critically relies on efficient digital signal processing (DSP). We demonstrate a lite DSP scheme to reduce the transmission cost and power consumption, which is mainly realized by reducing the sampling rate and simplifying the DSP algorithm. On the one hand, the baud-rate sampling technique based on the integral circuit can reduce the amount of data processing in DSP. On the other hand, we proposed a simplified joint modified constant modulus algorithm (MCMA) and phase-dependent decision-directed least mean square (DD-LMS) algorithm for adaptive blind polarization demultiplexing and phase recovery in which the butterfly structure is no longer needed for DD-LMS. And we compare the proposed simplified algorithm with the joint traditional CMA and blind phase search and the MCMA, in terms of performance in the 80-Gbaud dual-polarization 64QAM homodyne detection system. The results show that the proposed lite DSP mechanism can effectively reduce the power consumption of DSP by sub-rate sampling and simplifying the corresponding algorithm, which provides an alternative scheme for low-power optical interconnection of data centers.