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We study the secure decentralized Pliable Index CODing (PICOD) problem withcircular side information sets at the users. The security constraint forbidsevery user to decode more than one message while a decentralized setting meansthere is no central transmitter in the system. Compared to the secure butcentralized version of the problem, a converse bound from one of our previousworks showed a factor of three difference in optimal code length under theconstraint of linear encoding. In this paper, we first list the linearlyinfeasible cases, that is, problems where no linear code can simultaneouslyachieve both correctness/decodability and security. Then, we propose linearcoding schemes for all remaining cases and show that their attained code lengthis to within an additive constant gap from our converse bound.

Optimal Linear Coding Schemes for the Secure Decentralized Pliable Index Coding Problem