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 \textit{CRT lattice index 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.

翻译：索引编码问题旨在通过利用接收端边信息来提升传输效率，从而优化广播通信。本文探讨了Construction $\pi_A$格在索引编码中的应用。我们提出了一种名为\textit{CRT格索引编码}的编码方案，该方案在$\mathbb{Z}$上使用Construction $\pi_A$来解决索引编码问题。我们推导了CRT格索引码边信息增益的上界，并给出了该增益均匀性的条件。通过理论分析和编码设计实例，验证了该方法的有效性。