In this work we study the rate-distortion function (RDF) for lossy compression of asynchronously-sampled continuous-time (CT) wide-sense cyclostationary (WSCS) Gaussian processes with memory. As the case of synchronous sampling, i.e., when the sampling interval is commensurate with the period of the cyclostationary statistics, has already been studied, we focus on discrete-time (DT) processes obtained by asynchronous sampling, i.e., when the sampling interval is incommensurate with the period of the cyclostationary statistics of the CT WSCS source process. It is further assumed that the sampling interval is smaller than the maximal autocorrelation length of the CT source process, which implies that the DT process possesses memory. Thus, the sampled process is a DT wide-sense almost cyclostationary (WSACS) processes with memory. This problem is motivated by the fact that man-made communications signals are modelled as CT WSCS processes; hence, applications of such sampling include, e.g., compress-and-forward relaying and recording systems. The main challenge follows because, with asynchronous sampling, the DT sampled process is not information-stable, and hence the characterization of its RDF should be carried out within the information-spectrum framework instead of using conventional information-theoretic arguments. This work expands upon our previous work which addressed the special case in which the DT process is independent across time. The existence of dependence between the samples requires new tools to obtain the characterization of the RDF.

翻译：本文研究了具有记忆的连续时间宽平稳循环平稳高斯过程在异步采样下有损压缩的率失真函数。由于同步采样（即采样间隔与循环平稳统计量的周期可公度）的情形已有研究，我们聚焦于通过异步采样（即采样间隔与连续时间宽平稳循环平稳源过程的循环平稳统计量周期不可公度）获得的离散时间过程。进一步假设采样间隔小于连续时间源过程的最大自相关长度，这意味着离散时间过程具有记忆性。因此，采样后的过程是具备记忆的离散时间宽平稳近似循环平稳过程。该问题的研究动机在于人造通信信号通常建模为连续时间宽平稳循环平稳过程；因此，此类采样的应用包括压缩转发中继与记录系统等。主要挑战源于异步采样下离散时间采样过程不具备信息稳定性，因而其率失真函数的刻画需在信息谱框架内进行，而非使用传统信息论方法。本文在我们先前针对离散时间过程各时刻独立这一特殊情形的研究基础上进行了扩展。样本间依赖关系的存在需要新的工具来获得率失真函数的刻画。