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：本文研究异步采样的连续时间（CT）宽义循环平稳（WSCS）高斯过程在存在记忆性情况下的有损压缩率失真函数（RDF）。鉴于同步采样（即采样间隔与循环平稳统计量的周期可公度）的情况已有研究，我们重点分析通过异步采样（即采样间隔与CT WSCS源过程的循环平稳统计量周期不可公度）获得的离散时间（DT）过程。进一步假设采样间隔小于CT源过程的最大自相关长度，这意味着DT过程具有记忆性。因此，采样过程是一个具有记忆的离散时间宽义近似循环平稳（WSACS）过程。该问题的动机源于：人为通信信号通常被建模为CT WSCS过程，因此此类采样的应用包括如压缩-转发中继和记录系统。主要挑战在于：异步采样导致DT采样过程非信息稳定，因此其RDF的表征需在信息谱框架内进行，而非采用传统信息论方法。本文扩展了我们先前针对DT过程在时间上独立这一特殊情形的研究工作。样本间的依赖关系需要引入新工具才能获得RDF的表征。