Recent efforts in neural compression have focused on the rate-distortion-perception (RDP) tradeoff, where the perception constraint ensures the source and reconstruction distributions are close in terms of a statistical divergence. Theoretical work on RDP describes properties of RDP-optimal compressors without providing constructive and low complexity solutions. While classical rate-distortion theory shows that optimal compressors should efficiently pack space, RDP theory additionally shows that infinite randomness shared between the encoder and decoder may be necessary for RDP optimality. In this paper, we propose neural compressors that are low complexity and benefit from high packing efficiency through lattice coding and shared randomness through shared dithering over the lattice cells. For two important settings, namely infinite shared and zero shared randomness, we analyze the RDP tradeoff achieved by our proposed neural compressors and show optimality in both cases. Experimentally, we investigate the roles that these two components of our design, lattice coding and randomness, play in the performance of neural compressors on synthetic and real-world data. We observe that performance improves with more shared randomness and better lattice packing.

From a technical perspective, the n ew perception constraint is not conducive to single-letteriz ation; in fact, single-letterization appears to be impossi ble for a generic divergence φ. From an operational standpoint, it has been observed that u nder the perception constraint (8), the fundamental performance limits are generally not characterized by Blau and Michaeli's distortion-rate-perception function D (R,P); more surprisingly, they critically depend on the amount of commo n randomness shared between the encoder and decoder [5]-[8], whereas common randomness is known [4] to have no impact on th e performance limits under the perception constraint (7).

Recent efforts in neural compression have focused on the rate-distortion-perception (RDP) tradeoff, where the perception constraint ensures the source and reconstruction distributions are close in terms of a statistical divergence. Theoretical work on RDP describes interesting properties of RDP-optimal compressors without providing constructive and low complexity solutions. While classical rate distortion theory shows that optimal compressors should efficiently pack the space, RDP theory additionally shows that infinite randomness shared between the encoder and decoder may be necessary for RDP optimality. In this paper, we propose neural compressors that are low complexity and benefit from high packing efficiency through lattice coding and shared randomness through shared dithering over the lattice cells. For two important settings, namely infinite shared and zero shared randomness, we analyze the rate, distortion, and perception achieved by our proposed neural compressors and further show optimality in the presence of infinite shared randomness. Experimentally, we investigate the roles these two components of our design, lattice coding and randomness, play in the performance of neural compressors on synthetic and real-world data. We observe that performance improves with more shared randomness and better lattice packing.

The distortion-rate function of output-constrained lossy source coding with limited common randomness is analyzed for the special case of squared error distortion measure. An explicit expression is obtained when both source and reconstruction distributions are Gaussian. This further leads to a partial characterization of the information-theoretic limit of quadratic Gaussian rate-distortion-perception coding with the perception measure given by Kullback-Leibler divergence or squared quadratic Wasserstein distance.

Semantic communication has attracted significant interest recently due to its capability to meet the fast growing demand on user-defined and human-oriented communication services such as holographic communications, eXtended reality (XR), and human-to-machine interactions. Unfortunately, recent study suggests that the traditional Shannon information theory, focusing mainly on delivering semantic-agnostic symbols, will not be sufficient to investigate the semantic-level perceptual quality of the recovered messages at the receiver. In this paper, we study the achievable data rate of semantic communication under the symbol distortion and semantic perception constraints. Motivated by the fact that the semantic information generally involves rich intrinsic knowledge that cannot always be directly observed by the encoder, we consider a semantic information source that can only be indirectly sensed by the encoder. Both encoder and decoder can access to various types of side information that may be closely related to the user's communication preference. We derive the achievable region that characterizes the tradeoff among the data rate, symbol distortion, and semantic perception, which is then theoretically proved to be achievable by a stochastic coding scheme. We derive a closed-form achievable rate for binary semantic information source under any given distortion and perception constraints. We observe that there exists cases that the receiver can directly infer the semantic information source satisfying certain distortion and perception constraints without requiring any data communication from the transmitter. Experimental results based on the image semantic source signal have been presented to verify our theoretical observations.

In this paper, we study the computation of the rate-distortion-perception function (RDPF) for a multivariate Gaussian source under mean squared error (MSE) distortion and, respectively, Kullback-Leibler divergence, geometric Jensen-Shannon divergence, squared Hellinger distance, and squared Wasserstein-2 distance perception metrics. To this end, we first characterize the analytical bounds of the scalar Gaussian RDPF for the aforementioned divergence functions, also providing the RDPF-achieving forward "test-channel" realization. Focusing on the multivariate case, we establish that, for tensorizable distortion and perception metrics, the optimal solution resides on the vector space spanned by the eigenvector of the source covariance matrix. Consequently, the multivariate optimization problem can be expressed as a function of the scalar Gaussian RDPFs of the source marginals, constrained by global distortion and perception levels. Leveraging this characterization, we design an alternating minimization scheme based on the block nonlinear Gauss-Seidel method, which optimally solves the problem while identifying the Gaussian RDPF-achieving realization. Furthermore, the associated algorithmic embodiment is provided, as well as the convergence and the rate of convergence characterization. Lastly, for the "perfect realism" regime, the analytical solution for the multivariate Gaussian RDPF is obtained. We corroborate our results with numerical simulations and draw connections to existing results.

Lossy compression algorithms are typically designed to achieve the lowest possible distortion at a given bit rate. However, recent studies show that pursuing high perceptual quality would lead to increase of the lowest achievable distortion (e.g., MSE). This paper provides nontrivial results theoretically revealing that, \textit{1}) the cost of achieving perfect perception quality is exactly a doubling of the lowest achievable MSE distortion, \textit{2}) an optimal encoder for the "classic" rate-distortion problem is also optimal for the perceptual compression problem, \textit{3}) distortion loss is unnecessary for training a perceptual decoder. Further, we propose a novel training framework to achieve the lowest MSE distortion under perfect perception constraint at a given bit rate. This framework uses a GAN with discriminator conditioned on an MSE-optimized encoder, which is superior over the traditional framework using distortion plus adversarial loss. Experiments are provided to verify the theoretical finding and demonstrate the superiority of the proposed training framework.