标题： 具有记忆和有界处理延迟的采样循环平稳高斯过程的率失真函数：包含证明的扩展版本 显示英文标题

标题： The Rate-Distortion Function for Sampled Cyclostationary Gaussian Processes with Memory and with Bounded Processing Delay: Extended Version with Proofs

摘要： 我们研究了离散时间（DT）广义几乎周期平稳（WSACS）高斯过程在有记忆情况下的率失真函数（RDF），这些过程来源于连续时间（CT）广义周期平稳（WSCS）高斯信源过程的采样。 这个问题的重要性在于这样的CT过程代表了通信信号，必须进行采样以促进与其压缩相关的DT处理。 此外，振荡器的物理特性意味着采样间隔与物理过程的自相关函数（AF）的周期不相容，从而产生了所考虑的DT WSACS模型。 另外，为了减少损失，采样间隔通常比相关长度短，因此DT过程也是相关的。 RDF表征的困难来自于WSACS过程的信息不稳定，这使得传统的信息论工具不可用。 在本工作中，我们利用信息谱框架来表征当允许后续源序列处理之间存在有限且有界的延迟时的RDF。 这种场景扩展了我们之前的研究，这些研究探讨了没有处理延迟或没有记忆的情况。 数值评估揭示了异步采样下场景参数对RDF的影响。 显示英文摘要

摘要： We study the rate-distortion function (RDF) for the lossy compression of discrete-time (DT) wide-sense almost cyclostationary (WSACS) Gaussian processes with memory, arising from sampling continuous-time (CT) wide-sense cyclostationary (WSCS) Gaussian source processes. The importance of this problem arises as such CT processes represent communications signals, and sampling must be applied to facilitate the DT processing associated with their compression. Moreover, the physical characteristics of oscillators imply that the sampling interval is incommensurate with the period of the autocorrelation function (AF) of the physical process, giving rise to the DT WSACS model considered. In addition, to reduce the loss, the sampling interval is generally shorter than the correlation length, and thus, the DT process is correlated as well. The difficulty in the RDF characterization follows from the information-instability of WSACS processes, which renders the traditional information-theoretic tools inapplicable. In this work we utilize the information-spectrum framework to characterize the RDF when a finite and bounded delay is allowed between processing of subsequent source sequences. This scenario extends our previous works which studied settings without processing delays or without memory. Numerical evaluations reveal the impact of scenario parameters on the RDF with asynchronous sampling.