  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.
