An Embedded Index Code Construction Using Sub-packetization
Shanuja Sasi, Vaneet Aggarwal, and B. Sundar Rajan

TL;DR
This paper introduces a novel sub-packetization-based code construction for the Consective and Symmetric Embedded Index Coding Problem (CS-EICP), achieving lower normalized rates than previous scalar linear solutions.
Contribution
It presents a new sub-packetization approach for CS-EICP, improving upon prior scalar linear code constructions by reducing the normalized transmission rate.
Findings
Normalized rate is lower than previous scalar linear codes.
Sub-packetization offers a new coding strategy for CS-EICP.
Explicit code construction demonstrated for CS-EICP.
Abstract
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…
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