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The recently reported high spectral efficiency (SE) and high-baud-rate signal transmission are all based on digital coherent optical communications and digital signal processing (DSP). DSP simplifies the reception of advanced modulation formats and also enables the major electrical and optical impairments to be processed and compensated in the digital domain, at the transmitter or receiver side. In this paper, we summarize the research progress on high-speed signal generation and detection and also show the progress on DSP for high-speed signal detection. We also report the latest progress on multi-core and multi-mode multiplexing.