The use of sensor applications has been steadily increasing, leading to an urgent need for efficient data compression techniques to facilitate the storage, transmission, and processing of digital signals generated by sensors. Unlike other sequential data such as text sequences, sensor signals have more complex statistical characteristics. Specifically, in every signal point, each bit, which corresponds to a specific precision scale, follows its own conditional distribution depending on its history and even other bits. Therefore, applying existing general-purpose data compressors usually leads to a relatively low compression ratio, since these compressors do not fully exploit such internal features. What is worse, partitioning a bit stream into groups with a preset size will sometimes break the integrity of each signal point. In this paper, we present a lossless data compressor dedicated to compressing sensor signals which is built upon a novel recurrent neural architecture named multi-channel recurrent unit (MCRU). Each channel in the proposed MCRU models a specific precision range of each signal point without breaking data integrity. During compressing and decompressing, the mirrored network will be trained on observed data; thus, no pre-training is needed. The superiority of our approach over other compressors is demonstrated experimentally on various types of sensor signals.