Memoryless Sampling Rate Distortion

Consider a discrete memoryless multiple source with m component sources. A subset of k <= m sources are sampled at each time instant and jointly compressed in order to reconstruct all the m sources under a given distortion criterion. A sampling rate distortion function is characterized for the case of memoryless random sampling with the sampler possibly depending on the source outputs; and the decoder is informed of the sequence of sampled sets. Examining the structure of the optimal sampler, it is shown that deterministic sampling, characterized by a conditional point-mass, suffices. Restricted forms of sampling are also addressed. An upper bound for the sampling rate distortion function is provided when the decoder is not informed of the sequence of sampled sets.