We introduce a new operational technique for deriving chain rules for general information theoretic quantities. This technique is very different from the popular (and in some cases fairly involved) methods like SDP formulation and operator algebra or norm interpolation. Instead, our framework considers a simple information transmission task and obtains lower and upper bounds for it. The lower bounds are obtained by leveraging a successive cancellation encoding and decoding technique. Pitting the upper and lower bounds against each other gives us the desired chain rule. As a demonstration of this technique, we derive chain rules for the smooth max mutual information and the smooth-Hypothesis testing mutual information.

翻译：我们引入了一种新的操作方法，用于推导一般信息论量的链式法则。该方法与流行的（在某些情况下相当复杂的）技术（如SDP公式化、算子代数或范数插值）截然不同。相反，我们的框架考虑一个简单的信息传输任务，并为其建立上下界。下界通过利用逐次抵消编码与解码技术获得。将上下界相互制约，即可得到所需的链式法则。作为该方法的演示，我们推导了平滑最大互信息和平滑假设检验互信息的链式法则。