We develop the notion of a locally homomorphic channel and prove an approximate equivalence between those and codes for computing functions. Further, we derive decomposition properties of locally homomorphic channels which we use to analyze and construct codes where two messages must be encoded independently. This leads to new results for identification and K-identification when all messages are sent over multiple-access channels, which yield surprising rate improvements compared to naive code constructions. In particular, we demonstrate that for the example of identification with deterministic encoders, both encoders can be constructed independently.

翻译：我们发展了局部同态信道的概念，并证明了其与函数计算编码之间的近似等价性。进一步，我们推导了局部同态信道的分解性质，并利用这些性质分析并构建了需独立编码两个消息的编码方案。这为所有消息通过多址接入信道传输时的识别与K-识别问题带来了新结果，与朴素编码构造相比，这些结果在速率上实现了显著提升。特别地，我们证明在确定型编码器的识别示例中，两个编码器可以独立构造。