Harnessing a block-sparse prior to recover signals through underdetermined linear measurements has been extensively shown to allow exact recovery in conditions where classical compressed sensing would provably fail. We exploit this result to propose a novel private communication framework where the secrecy is achieved by transmitting instances of an unidentifiable compressed sensing problem over a public channel. The legitimate receiver can attempt to overcome this ill-posedness by leveraging secret knowledge of a block structure that was used to encode the transmitter's message. We study the privacy guarantees of this communication protocol to a single transmission, and to multiple transmissions without refreshing the shared secret. Additionally, we propose an algorithm for an eavesdropper to learn the block structure via the method of moments and highlight the privacy benefits of this framework through numerical experiments.

翻译：在通过不确定的线性测量恢复信号之前先利用一个块状裂缝,已经广泛证明,以便在古典压缩感测可能失败的情况下能够准确恢复; 我们利用这一结果提出一个新的私人通信框架,通过在公共频道上传输无法识别的压缩感测问题,从而实现保密; 合法接收者可以通过利用用于将发射器电文编码的块状结构的秘密知识,试图克服这种错误的隐蔽性; 我们研究这一通信协议的隐私保障,即单一传输和多次传输,而不刷新共同的秘密。 此外,我们建议为窃听者提供一种算法,以便通过时间方法了解块状结构,并通过数字实验突出这一框架的隐私利益。