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 with vanishing error probability. Analog transmitters hold sequences of analog values, and some functions of these distributed values (but not the values themselves) need to be conveyed to the receiver, subject to a fidelity criterion such as mean squared error (MSE) or a certain maximum error with 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 result to a class of functions that includes all linear and some non-linear functions. The practicality of our proposed communication scheme is shown in channel simulations that use a version of the scheme based on low density parity check (LDPC) coding and evaluate the system performance for different block lengths and Gaussian as well as non-Gaussian noise distributions.

翻译：针对高斯多址接入信道（MAC），我们研究了包含两类发射机的通信场景：数字发射机持有离散集合中的消息，需以渐近可忽略的差错概率传输至接收端；模拟发射机持有模拟数值序列，这些分布式数值的某些函数（而非数值本身）需在均方误差（MSE）或给定置信度下的特定最大误差等保真度准则下传输至接收端。针对模拟发射机需计算的函数为取值在[-1,1]内的数值之和的情形，我们在数字发射机受峰值与平均功率约束、模拟发射机受峰值功率约束的条件下，推导了数字与模拟通信速率折中的内界与外界。随后我们将可达性结果推广至包含所有线性函数及部分非线性函数的一类函数。通过基于低密度奇偶校验（LDPC）编码的通信方案版本，针对不同块长度以及高斯与非高斯噪声分布评估系统性能的信道仿真，验证了所提通信方案的实用性。