In Private Information Retrieval (PIR), one wants to download a file from a
database without revealing to the database which file is being downloaded. Much
attention has been paid to the case of the database being encoded across
several servers, subsets of which can collude to attempt to deduce the
requested file. With the goal of studying the achievable PIR rates in realistic
scenarios, we generalize results for coded data from the case of all subsets of
servers of size t colluding, to arbitrary subsets of the servers. We
investigate the effectiveness of previous strategies in this new scenario, and
present new results in the case where the servers are partitioned into disjoint
colluding groups.Comment: Updated with a corrected statement of Theorem
