Private Information Retrieval from Multiple Access Channels

We consider the private information retrieval problem from multiple access channels (MAC-PIR). In MAC-PIR, there areN databases, each storing the same set of M messages. The database responses reach the user through a multiple access channel (MAC) that may mix the responses together in a stochastic way. We show that for the additive MAC and the conjunction/disjunction MAC, channel coding and retrieval scheme are inseparable unlike the noisy private information retrieval problem (NPIR). We show that the retrieval scheme depends on the properties of the MAC, in particular on the linearity aspect. For both cases, we provide schemes that achieve the full capacity without any loss due to the privacy constraint, which implies that the user can exploit the nature of the channel in its favor. Finally, we show that the full capacity is not always attainable by determining the capacity of the selection channel.