The problem of transmitting a parameter value over an additive white Gaussian noise (AWGN) channel is considered, where, in addition to the transmitter and the receiver, there is a helper that observes the noise non-causally and provides a description of limited rate $R_h$ to the transmitter and/or the receiver. We derive upper and lower bounds on the optimal achievable $\alpha$-th moment of the estimation error and show that they coincide for small values of $\alpha$ and for high values of $R_h$. The upper bound relies on a recently proposed channel-coding scheme that effectively conveys $R_h$ bits essentially error-free and the rest of the rate - over the same AWGN channel without help, with the error-free bits being allocated to the most significant bits of the quantized parameter. We then concentrate on the setting with a total transmit energy constraint, for which we derive achievability results for both channel coding and parameter modulation for several scenarios: when the helper assists only the transmitter or only the receiver and knows the noise, and when the helper assists the transmitter and/or the receiver and knows both the noise and the message. In particular, for the message-informed helper that assists both the receiver and the transmitter, it is shown that the error probability in the channel-coding task decays doubly exponentially. Finally, we translate these results to those for continuous-time power-limited AWGN channels with unconstrained bandwidth. As a byproduct, we show that the capacity with a message-informed helper that is available only at the transmitter can exceed the sum of the capacity without help and the help rate $R_h$, when the helper knows only the noise but not the message.

翻译：考虑在加性高斯白噪声（AWGN）信道上传输参数值的问题，其中除了发送端和接收端外，还存在一个辅助者，该辅助者非因果地观测噪声，并以有限速率$R_h$向发送端和/或接收端提供描述。我们推导了最优可达$\alpha$次估计误差矩的上界和下界，并证明当$\alpha$较小以及$R_h$较高时，这些界是重合的。上界依赖于最近提出的一种信道编码方案，该方案能以基本无差错的方式有效传输$R_h$比特，而剩余速率则通过同一无辅助的AWGN信道传输，其中无差错比特被分配给量化参数的最高有效位。随后，我们聚焦于具有总发射能量约束的场景，针对以下几种情形推导了信道编码和参数调制的可达性结果：辅助者仅协助发送端或仅协助接收端且知晓噪声时，以及辅助者协助发送端和/或接收端且同时知晓噪声与消息时。特别地，对于协助接收端和发送端的信息知情辅助者，我们证明信道编码任务中的错误概率呈双指数衰减。最后，我们将这些结果转化为连续时间、带宽不受限、功率受限的AWGN信道下的结论。作为副产品，我们证明当辅助者仅知晓噪声而不知晓消息时，仅作用于发送端的信息知情辅助者所能达到的信道容量，有可能超过无辅助容量与辅助速率$R_h$之和。