An Embedded Index Code Construction Using Sub-packetization

A variant of the index coding problem (ICP), the embedded index coding problem (EICP) was introduced in [A. Porter and M. Wootters, "Embedded Index Coding," ITW, Sweden, 2019] which was motivated by its application in distributed computing where every user can act as sender for other users and an algorithm for code construction was reported. The construction depends on the computation of minrank of a matrix, which is computationally intensive. In [A.A. Mahesh, N. S. Karat and B. S. Rajan, "Min-rank of Embedded Index Coding Problems," ISIT, 2020], the authors have provided an explicit code construction for a class of EICP - Consecutive and Symmetric Embedded Index Coding Problem (CS-EICP). We introduce the idea of sub-packetization of the messages in index coding problems to provide a novel code construction for CSEICP in contrast to the scalar linear solutions provided in the prior works. For CS-EICP, the normalized rate, which is defined as the number of bits transmitted by all the users together normalized by the total number of bits of all the messages, for our construction is lesser than the normalized rate achieved by Mahesh et al., for scalar linear codes.