The task of jointly communicating a message and reconstructing a common estimate of the channel state is examined for a fading Gaussian model with additive state interference. The state is an independent and identically distributed Gaussian sequence known noncausally at the transmitter, and the instantaneous fading coefficient is perfectly known at both the transmitter and the receiver. The receiver is required to decode the transmitted message and, in addition, reconstruct the state under a common reconstruction constraint ensuring that its estimate coincides with that at the transmitter. A complete characterization of the optimal rate distortion tradeoff region for this setting is the main result of our work. The analytical results are also validated through numerical examples illustrating the rate distortion and power distortion tradeoffs.

翻译：本文研究了在具有加性状态干扰的衰落高斯模型中，联合传输消息并重构信道状态公共估计的任务。状态是一个独立同分布的高斯序列，在发送端非因果已知，而瞬时衰落系数在发送端和接收端均完美已知。接收端不仅需要解码传输的消息，还需在公共重构约束下重构状态，该约束确保其估计与发送端估计一致。本文的主要成果是完全刻画了该场景下的最优率失真权衡区域。分析结果还通过数值算例进行了验证，阐明了率失真与功率失真的权衡关系。