The index coding problem is a problem of efficient broadcasting with side-information. In uniprior index coding, the sets of side-information symbols possessed by different receivers are disjoint. For single uniprior index coding, in which each receiver has a single unique side-information symbol, a polynomial complexity construction of an optimal index code is known from prior work. In this work, we model the uniprior index coding problem as a supergraph, and focus on a class of uniprior problems defined on special supergraphs known as generalized cycles in which the sizes of the demand set and the side-information set are equal at each receiver. For such problems, we prove upper and lower bounds on the optimal broadcast rate. Using a connection with Eulerian directed graphs, we also show that the upper and lower bounds are equal for a subclass of uniprior problems. We show the NP-hardness of finding the lower bound for uniprior problems on generalized cycles, hence contrasting such uniprior problems with single uniprior problems. Finally, we look at a simple extension of the generalized cycle uniprior class for which we give bounds on the optimal rate and show an explicit scheme which achieves the upper bound.
Several algebraic and graph-theoretic index code constructions are available, and upper and lower bounds are known for the minimum block length of an index code; see, for example, [1]- REF .
Uniprior index coding
2017 IEEE International Symposium on Information Theory (ISIT)
2017 IEEE International Symposium on Information Theory (ISIT)
Mathematics Computer Science