Canonical description for multiterminal source coding

Principles behind lossless and lossy coding are usually considered related, yet distinct. In contrast, we show that the direct statements of the rate-distortion theorem and the lossless coding theorem are consequences of a common distortion-abstracted phenomenon. Significantly, we extend such distortion abstraction to a more general multiterminal framework, and derive a canonical direct theorem that subsumes known results. Further, we show that the converse holds if all but at most one encoded sources are perfectly reconstructed, and, thereby, not only generalize known results but settle open problems such as the single-helper problem. More generally, a canonical sequence of inner bounds approaches the achievable region, and points to a new problem, whose solution, if found, would lead to a desirable computable description.