Index Coding with Coded Side-Information

TL;DR

This paper introduces a new class of index coding problems involving coded side-information, characterizes the optimal code length using matrix minrank, and proposes a greedy algorithm to minimize this length.

Contribution

It extends the concept of matrix minrank to coded side-information and provides a method to compute the optimal index code length.

Findings

Optimal binary vector index code length equals the minimum rank of a specific matrix.

Derived an expression for the minimum index code length in the presence of coded side-information.

Proposed a greedy randomized algorithm to minimize the matrix rank and thus the code length.

Abstract

This letter investigates a new class of index coding problems. One sender broadcasts packets to multiple users, each desiring a subset, by exploiting prior knowledge of linear combinations of packets. We refer to this class of problems as index coding with coded side-information. Our aim is to characterize the minimum index code length that the sender needs to transmit to simultaneously satisfy all user requests. We show that the optimal binary vector index code length is equal to the minimum rank (minrank) of a matrix whose elements consist of the sets of desired packet indices and side- information encoding matrices. This is the natural extension of matrix minrank in the presence of coded side information. Using the derived expression, we propose a greedy randomized algorithm to minimize the rank of the derived matrix.