Min-rank of Embedded Index Coding Problems

For the problem of embedded index coding, a matrix representation, called a side-information matrix and a metric called min-rank are defined to characterize the length of an optimal embedded index code. An optimal embedded index code for a given embedded index coding problem is shown to be obtainable from the columns of its side information matrix. Further, for a class of embedded index coding problems, called one-sided neighboring side information problems, the min-rank is derived and a transmission scheme which has length equal to this min-rank is presented.