In this paper, we experimentally demonstrate a 5 GBaud four-state continuous-variable quantum key distribution with digital signal processing. By employing a frequency- and polarization-multiplexing quantum key transceiver, the modulation noise and DAC quantization noise in quantum state preparation, the photo-leakage noise in co-fiber transmission, the detection noise and ADC quantization noise in polarization diversity detection can be effectively reduced for achieving an ultra-low level of excess noise. Moreover, the main polarization variation and phase noise can be accurately compensated by designing a precise digital compensation scheme including the pilot-assisted polarization and phase compensation algorithm and the data-assisted equalized compensation algorithm. Besides, the explicit asymptotic secure key rate is evaluated by using an improved semidefinite programming security analysis method, which achieves a 100 Mbps level of secure key rate within 10 km distance.
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