Achieving uniform side information gain with multilevel lattice codes over the ring of integers

The index coding problem aims to optimise broadcast communication by taking advantage of receiver-side information to improve transmission efficiency. In this letter, we explore the application of Construction ${\pi }_A$ lattices to index coding. We introduce a coding scheme, named $\mathit{\text{CRT}}\mathit{\text{lattice}}\mathit{\text{index}}\mathit{\text{coding}}$, using Construction ${\pi }_A$ over $\mathbb{Z}$ to address the index coding problem. It is derived an upper bound for side information gain of a CRT lattice index code and conditions for the uniformity of this gain. The efficiency of this approach is shown through theoretical analysis and code design examples.