  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 constructions depends on the
computation of minrank of a matrix, which is computationally intensive. In [A.
Mahesh, N. Sageer Karat and B. S. Rajan, "Min-rank of Embedded Index Coding
Problems," ISIT, 2020], for EICP, a notion of side-information matrix was
introduced and it was proved that the length of an optimal scalar linear index
code is equal to the min-rank of the side-information matrix. The authors have
provided an explicit code construction for a class of EICP -
\textit{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 CS-EICP 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.
