We devise achievable encoding schemes for distributed source compression for computing inner products, symmetric matrix products, and more generally, square matrix products, which are a class of nonlinear transformations. To that end, our approach relies on devising nonlinear mappings of distributed sources, which are then followed by the structured linear encoding scheme, introduced by K\"orner and Marton. For different computation scenarios, we contrast our findings on the achievable sum rate with the state of the art to demonstrate the possible savings in compression rate. When the sources have special correlation structures, it is possible to achieve unbounded gains, as demonstrated by the analysis and numerical simulations.

翻译：我们设计了用于分布式源编码的可实现编码方案，以计算内积、对称矩阵乘积以及更一般的方阵乘积（属于一类非线性变换）。为此，我们的方法依赖于设计分布式源的非线性映射，随后采用Körner和Marton提出的结构化线性编码方案。针对不同的计算场景，我们将可实现的编码总速率与现有技术进行对比，以展示压缩速率的潜在节省空间。当源数据具有特殊的相关结构时，分析和数值模拟表明可实现无界增益。