A k-server Private Information Retrieval (PIR) code is a binary linear [m, s]-code admitting a generator matrix such that for every integer i with 1≤i≤s there exist k disjoint subsets of columns (called recovery sets) that add up to the vector of weight one, with the single 1 in position i. A k-server PIR code is useful to reduce the storage overhead of a traditional k-server PIR protocol. Finding k-server PIR codes with a small blocklength for a given dimension has recently become an important research challenge. In this work, we propose new constructions of PIR codes from combinatorial structures, introducing the notion of k-partial packing. Several bounds over the existing literature are improved.
PIR Codes from Combinatorial Structures
Giulietti, Massimo;Timpanella, Marco
2023
Abstract
A k-server Private Information Retrieval (PIR) code is a binary linear [m, s]-code admitting a generator matrix such that for every integer i with 1≤i≤s there exist k disjoint subsets of columns (called recovery sets) that add up to the vector of weight one, with the single 1 in position i. A k-server PIR code is useful to reduce the storage overhead of a traditional k-server PIR protocol. Finding k-server PIR codes with a small blocklength for a given dimension has recently become an important research challenge. In this work, we propose new constructions of PIR codes from combinatorial structures, introducing the notion of k-partial packing. Several bounds over the existing literature are improved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
