mmWave technology is set to become a main feature of next generation wireless networks, e.g., 5G mobile and WiFi 802.11ad/ay. Among the basic and most fundamental challenges facing mmWave is the ability to overcome its unfavorable propagation characteristics using energy efficient solutions. This has been addressed using innovative transceiver architectures. However, these architectures have their own limitations when it comes to channel estimation. This paper focuses on channel estimation and poses it as a source compression problem, where channel measurements are designed to mimic an encoded (compressed) version of the channel. We show that linear source codes can significantly reduce the number of channel measurements required to discover all channel paths. We also propose a deep-learning-based approach for decoding the obtained measurements, which enables high-speed and efficient channel discovery.