The effect of distortion on the MDL model

We investigate the consequences of lossy compression, i.e., description with distortion, on the model selection of the minimum description length (MDL) criterion. Our basic observation is that for a finite data sequence and sufficiently large distortion, a two-stage universal lossy encoder tends to under-estimate the model order of the source. We demonstrate this property by examining the behavior of a two-stage universal lossy encoder, based on pre/post-filtered entropy-coded dithered quantization, over some parametric classes of stationary Gaussian sources.