Information theoretic converse proofs for some PICOD problems

摘要

This paper provides information theoretic converse proofs for some classes of Pliable Index CODing (PICOD) problems. PICOD is a variant of the index coding problem in which a user is satisfied whenever it can successfully decode any one message that is not in its side information set. Past work on PICOD provided a number of achievable schemes based on linear codes, some of which are known to be optimal when the server is restricted to use linear codes only. This paper proves that for some of those cases linear codes are indeed optimal in an information theoretic sense, i.e., they cannot be beaten by non-linear codes. It also shows the information theoretic optimality for other classes of PICOD problems that were open.