Private Pliable Index Coding The Pliable Index CODing (PICOD) problem is a variant of the Index Coding (IC) problem, where the desired messages by the users, who are equipped with message side information, are part of the optimization. This paper studies the PICOD problem where users are subject to a privacy constraint. In particular, the following special class of private PICODs is investigated: 1) the side information structure is circular, and 2) each user can decode one and only one message. The first condition is a special case of the xe2x80x9ccirculararc network topology hypergraphxe2x80x9d class of PICOD studied in 6, for which an optimal solution was given without the privacy constraint. The second condition was first studied in 9 and was motivated by the need to keep content private in some distribution networks. This paper proposes both converse and achievable bounds. The proposed achievable scheme not only strictly outperforms the existing one for some values of the system parameters, but it is also information theoretically optimal in some settings. For the remaining cases, the proposed linear code is shown to require at most one more transmission than the best possible linear code.

A FieldSize Independent Code Construction for Groupcast Index Coding Problems The length of an optimal scalar linear index code of a groupcast index coding problem is equal to the minrank of its sideinformation hypergraph. The sideinformation hypergraph becomes a sideinformation graph for a special class of groupcast index coding problems known as unicast index coding problems. The number of computations required to find the minrank of a sideinformation graph depends on the number of edges present in the sideinformation graph. In this paper, we define the notion of minrankcritical edges in a sideinformation graph and derive some properties of minrank, which identifies minranknoncritical edges. Using these properties we present a method to reduce the number of computations required to compute minrank. Apart from this, we give a heuristic method to compute minrank. Also, we give an heuristic algorithm to find a clique cover of the sideinformation graph by using some binary operations on the adjacency matrix of the sideinformation graph. We also give a method to convert a groupcast index coding problem into a single unicast index coding problem. Combining all these results, we give a method to construct index codes (with not necessarily optimal length) for groupcast index coding problems. The construction technique is independent of field size and hence can be used to construct index codes over the binary field. In some cases the constructed index codes are better than the best known in the literature both in terms of the length of the code and the minimum field size required.