Lossy Subset Source Coding

This paper studies the lossy version of a problem recently proposed by the authors termed subset source coding, where the focus is on the fundamental limits of compression for subsets of the possible realizations of a discrete memoryless source. An upper bound is derived on the subset rate-distortion function in terms of the subset mutual information optimized over the set of conditional distributions that satisfy the expected distortion constraint with respect to the subset-typical distribution and over the set of certain auxiliary subsets. By proving a strong converse result, this upper bound is shown to be tight for a class of symmetric subsets. As illustrated in our numerical examples, more often than not, one achieves a gain in the fundamental limit, in that the optimal lossy compression rate for the subset can be strictly smaller than the rate-distortion function of the source, although exceptions can also be constructed.