On Multi-Message Private Computation
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In a typical formulation of the private information retrieval (PIR) problem, a single user wishes to retrieve one out of K datasets from N servers without revealing the demanded message index to any server. This paper formulates an extended model of PIR, referred to as multi-message private computation (MM-PC), where instead of retrieving a single message, the user wishes to retrieve P>1 linear combinations of datasets while preserving the privacy of the demand information. The MM-PC problem is a generalization of the private computation (PC) problem (where the user requests one linear combination of the datasets), and the multi-message private information retrieval (MM-PIR) problem (where the user requests P>1 datasets). A direct achievable scheme, referred to as baseline scheme, repeats the optimal PC scheme by Sun and Jafar P times, or treats each possible demanded linear combination as an independent dataset and then uses the near optimal MM-PIR scheme by Banawan and Ulukus. However, a direct combination of the PC and the MM-PIR schemes does not result in an achievable scheme. Our main contribution to this new problem is to propose an achievable MM-PC scheme by smartly leveraging the above two schemes with some additional highly non-trivial steps.
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