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A remarkable aspect of our upper bounds is a connection between SDMM and a form of private information retrieval (PIR) problem, known as multi-message X-secure T -private information retrieval (MM-XSTPIR).
Note that unlike PIR (private information retrieval) [3] problems there are no privacy constraints in SDMM, so users can publicly announce which matrix products they wish to retrieve.
A notable aspect of our upper bounds is a connection between SDMM and a form of private information retrieval (PIR) problem, known as multi-message X-secure T -private information retrieval (MM-XSTPIR).2 Interesting features of our achievable schemes include the idea of cross-subspace alignment that was introduced in [6] and was recently applied to SDMM in [7], and a novel transformation argument that converts a scalar multiplication problem into a scalar addition problem.
2Notably while the capacity of multi-message PIR has been explored in [4, 5] and that of X-secure T -private PIR has been explored in [6], to our knowledge there has been no prior work on MM-XSTPIR.
We prefer the formulation as a rate maximization because it allows a more direct connection to the capacity of PIR, one of the main themes of this work.
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