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 fixed sampling; and for independent and memoryless random sampling when the decoder is informed of the sequence of sampled sets. Inner bounds are provided when the decoder is uninformed. For jointly Gaussian sources under the mean-squared error criterion, a counterpart result for fixed sampling is given.