Some new results on index coding when the number of data is less than the number of receivers

Abstract

In this paper, index coding problems in which the number (m) of receivers is larger than that (n) of data are considered. Unlike the case that the two numbers are same (n = m), index coding problems with n ≤ m are more general and hard to handle. To circumvent this difficulty, problems with n <; m are approached via corresponding problems with n = m. It is shown that in certain cases, the symmetric capacity and code construction for index coding problems with n <; m can be obtained from the existing symmetric capacity result and codes for index coding problems with n = m. Such cases include cases with n <; m ≤ 5.