Achieving Uniform Side Information Gain With Multilevel Lattice Codes Over the Ring of Integers

The index coding problem aims to optimise broadcast communication by exploring side information available at the receivers. In this work, we investigate the use of Construction $\pi _{A}$ lattices over the ring of integers $\mathbb {Z}$ for index coding and establish algebraic conditions on the code generators to guarantee uniform side information gain. The effectiveness of the proposed approach is demonstrated through theoretical analysis and explicit code design examples.