采样、量化和编码：噪声信道上的实时估计
Sample, Quantize and Encode: Timely Estimation Over Noisy Channels
摘要：
量化和编码的高斯-马尔可夫过程的估计质量的影响被认为是，特别注意的Ornstein-Uhlenbeck过程。从该过程中获取样本，对其进行量化，然后使用无限增量冗余（IIR）或固定冗余（FR）编码方案进行编码以供传输。在接收机处消耗固定的处理时间用于解码和向发射机发送反馈。解码的消息被用来构建一个最小均方误差（MMSE）估计的过程作为时间的函数。这被证明是一个不断增长的功能的年龄的信息（AoI），定义为时间流逝，因为采样时间有关的最新成功解码的消息。该函数依赖于量化比特、码字长度和接收机处理时间。对于每个编码方案，目标是优化采样时间，使得长期平均MMSE最小化。然后，这是其特征在于设置一般增加泛函的AoI，不一定对应于MMSE，这可能是独立的利益在其他情况下。我们首先表明，IIR的最佳采样策略是这样的，只有当AoI超过一定的阈值时才生成新的样本，而对于FR，它是这样的，即当接收器完成处理前一个时，新的样本被及时发送。然后开发增强的传输方案，以便利用处理时间使新数据更快地在接收器处可用。对于IIR和FR，它表明，存在一个最佳数量的量化位，平衡AOI和量化误差，因此最小化的MMSE。它还表明，对于较长的接收机处理时间，相对简单的FR方案优于IIR。
英文摘要：
The effects of quantization and coding on the estimation quality of Gauss-Markov processes are considered, with a special attention to the Ornstein-Uhlenbeck process. Samples are acquired from the process, quantized, and then encoded for transmission using either infinite incremental redundancy (IIR) or fixed redundancy (FR) coding schemes. A fixed processing time is consumed at the receiver for decoding and sending feedback to the transmitter. Decoded messages are used to construct a minimum mean square error (MMSE) estimate of the process as a function of time. This is shown to be an increasing functional of the age-of-information (AoI), defined as the time elapsed since the sampling time pertaining to the latest successfully decoded message. Such functional depends on the quantization bits, codewords lengths and receiver processing time. The goal, for each coding scheme, is to optimize sampling times such that the long-term average MMSE is minimized. This is then characterized in the setting of general increasing functionals of AoI, not necessarily corresponding to MMSE, which may be of independent interest in other contexts. We first show that the optimal sampling policy for IIR is such that a new sample is generated only if the AoI exceeds a certain threshold, while for FR it is such that a new sample is delivered just-in-time as the receiver finishes processing the previous one. Enhanced transmissions schemes are then developed in order to exploit the processing times to make new data available at the receiver sooner. For both IIR and FR, it is shown that there exists an optimal number of quantization bits that balances AoI and quantization errors, and hence minimizes the MMSE. It is also shown that for longer receiver processing times, the relatively simpler FR scheme outperforms IIR.
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