Rate-Distortion Analysis for Sampled Correlated Cyclostationary Gaussian Processes

We study the rate-distortion function (RDF) for sampled cyclostationary Gaussian processes with memory, representing, e.g., the sampling of communications signals for the subsequent application of digital processing. Accounting for the inherent random jitter in local oscillators and keeping the sampling interval smaller than the memory length of the continuous-time (CT) source process to facilitate reliable modeling, induce a discrete-time (DT) wide-sense almost cyclostationary (WSACS) process with memory model upon the sampled signals. The main challenge follows from the information-instability of DT WSACS processes, which renders conventional information-theoretic approaches inapplicable. We use the information-spectrum framework to study the compression of incoming source sequences in two settings: when processing starts immediately upon reception and when a bounded delay exists between consecutive source sequences. Our analysis provides novel insights relating source memory, sampling frequency synchronization, and achievable compression rates.We show that, contrary to the sampled stationary case, the RDF for sampled cyclostationary processes is very sensitive to sampling rate synchronization. We also demonstrate that the RDF is not a monotonically decreasing function for the sampling rate and how introducing delay simplifies the compression scheme and lowers the rates.