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Multichannel audio signal is more difficult to be compressed than mono and stereo ones. A novel multichannel audio signal compression method based on tensor representation and decomposition is proposed in this paper. The multichannel audio is represented with 3-order tensor space and is decomposed into core tensor with three factor matrices in the way of channel, time and frequency. Only the truncated core tensor is transmitted which will be multiplied by the pre-trained factor matrices to reconstruct the original tensor space. Objective and subjective experiments have been done to show a very noticeable compression capability with an acceptable output quality. The novelty of the proposed compression method is that it enables both high compression capability and backward compatibility with limited signal distortion to the hearing.