We consider a rate-distortion problem with side information at multiple decoders. Several upper and lower bounds have been proposed for this general problem or special cases of it. We provide an upper bound for general instances of this problem, which takes the form of a linear program, by utilizing random binning and simultaneous decoding techniques [1] and compare it with the existing bounds. We also provide a lower bound for the general problem, which was inspired by a linear-programming lower bound for index coding, and show that it subsumes most of the lower bounds in literature. Using these upper and lower bounds, we explicitly characterize the rate-distortion function of a problem that can be seen as a Gaussian analogue of the “odd-cycle” index coding problem.

We provide a novel upper bound on the rate-distortion function with multiple decoders with side information, which takes the form of a linear program. This complements a recently-obtained lower bound that also takes the form of a linear program. We show that the upper bound is optimal in several instances of the problem1.

We consider rate-distortion with two decoders, each with distinct side information. This problem is well understood when the side information at the decoders satisfies a certain degradedness condition. We consider cases in which this degradedness condition is violated but the source and the side information consist of jointly Gaussian vectors. We provide a hierarchy of four lower bounds on the optimal rate. These bounds are then used to determine the optimal rate for several classes of instances.

We consider a rate distortion problem with side information at multiple decoders. Several lower bounds have been proposed for this general problem or special cases of it. We provide a lower bound for general instances of this problem, which was inspired by a linear-programming lower bound for index coding, and show that it subsumes most of the lower bounds in literature. Using this bound, we explicitly characterize the rate distortion function of a problem which can be seen as a Gaussian analogue of the “odd-cycle” index coding problem.

We approach index coding as a special case of rate–distortion with multiple receivers, each with some side information about the source. Specifically, using techniques developed for the rate–distortion problem, we provide two upper bounds and one lower bound on the optimal index coding rate. The upper bounds involve specific choices of the auxiliary random variables in the best existing scheme for the rate–distortion problem. The lower bound is based on a new lower bound for the general rate–distortion problem. The bounds are shown to coincide for a number of (groupcast) index coding instances, including all instances for which the number of decoders does not exceed three.

We investigate the rate-distortion region of a vector Gaussian source and two decoders with side information. We determine the rate-distortion region when both decoders have an error covariance distortion constraint that are scaled identity matrices.

The problem of general index coding with side information is investigated for the case of three receivers. We view the problem as a special case of lossy source coding with side information at the decoders, and we find the optimal rate.