The transmission on fronthaul links in the cloud radio access network has become a bottleneck with the increasing data rate. In this paper, we propose a novel two-stage compression scheme for fronthaul links. In the first stage, the commonly used techniques like cyclic prefix stripping and sampling rate adaptation are implemented. In the second stage, a structure called linear prediction coding with decision threshold (LPC-DT) is proposed to remove the redundancies of signal. Considering that the linear prediction outputs have large dynamic range, a two-piecewise quantization with optimized decision threshold is applied to enhance the quantization performance. In order to further lower the transmission rate, a multi-level successive structure of lossless polar source coding is proposed to compress the quantization output with low encoding and decoding complexity. Simulation results demonstrate that the proposed scheme with LPC-DT and LPSC offers not only significantly better compression ratios but also more flexibility in bandwidth settings compared with traditional ones.