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（这是一类非线性变换）。为此，我们的方法依赖于设计分布式源的非线性映射，随后采用由Kőrner和Marton提出的结构化线性编码方案。针对不同的计算场景，我们将关于可实现总码率的结果与现有技术进行对比，以展示压缩率可能带来的节省。当源具有特殊相关结构时，分析和数值模拟表明，可以实现无界增益。