We study communication over a Gaussian multiple-access channel (MAC) with two types of transmitters: Digital transmitters hold a message from a discrete set that needs to be communicated to the receiver. Analog transmitters hold sequences of analog values, and some function of these distributed values (but not the values themselves) need to be conveyed to the receiver. For the digital messages, it is required that they can be decoded error free at the receiver with high probability while the recovered analog function values have to satisfy a fidelity criterion such as an upper bound on mean squared error (MSE) or a certain maximum error with a given confidence. For the case in which the computed function for the analog transmitters is a sum of values in [-1,1], we derive inner and outer bounds for the tradeoff of digital and analog rates of communication under peak and average power constraints for digital transmitters and a peak power constraint for analog transmitters. We then extend the achievability part of our result to a larger class of functions that includes all linear, but also some non-linear functions.

翻译：我们研究高斯多址信道（MAC）上具有两类发射机的通信问题：数字发射机持有需要可靠传输给接收机的离散消息，而模拟发射机持有模拟值序列，需要将关于这些分布式值的某个函数（而非值本身）传递给接收机。对于数字消息，要求接收机能够以高概率无差错解码；对于恢复的模拟函数值，需满足保真度准则，例如均方误差（MSE）的上界或给定置信度下的特定最大误差。针对模拟发射机计算的函数为[-1,1]区间内数值之和的场景，我们推导了数字发射机在峰值与平均功率约束以及模拟发射机在峰值功率约束下，数字速率与模拟速率权衡的内外边界。随后，我们将结果的可达性部分推广至更广的函数类别，其中包含所有线性函数及部分非线性函数。