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LIT-812: Rate-Distortion-Perception Theory for Semantic Communication

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Properties4
StatusActive — read 2026-10-09 (NOTE-605); worth reading as a short statement of semantic communication as indirect (remote) source coding with a perception constraint: the encoder sees only a noisy observation X of the semantic source S, the decoder must reproduce S within an expected distortion and within a total-variation distance of S's distribution, and side information Y may help. It gives a rate region, a closed form for a doubly symmetric binary source, and an MNIST illustration. Read it knowing that it is a six-page workshop paper whose proofs are sketched or omitted, that the region as printed mixes channel and source terms and does not define the reconstruction, and that its "zero-rate recovery" is the familiar fact that a decoder with side information needs no bits once the tolerated distortion is what the side information alone achieves.
Tagsinformation-theory
Cited as “paper” byNOTE-605 — Rate-Distortion-Perception Theory for Semantic Communication
Cited as “source” byTHEORY-161 — In Zhao et al.'s (2025) and Chai et al.'s (2023) semantic rate–distortion frameworks, meaning is a latent variable with a known joint law with the observation, so their limits are indirect source-coding limits; Zhao et al.'s posterior-matching semantic distortion is, with KL divergence, exactly the information bottleneck, and with total variation a bound on the expected lost value of every bounded-loss decision

Graph View

Jingxuan Chai, Yong Xiao, Guangming Shi and Walid Saad (2023), 2023 IEEE 31st International Conference on Network Protocols (ICNP), workshop — ARXIV-2312.05437

Key takeaways

  • The model (Section III). A semantic source S, i.i.d.; the encoder sees k indirect observations X drawn through p(X|S); encoder and decoder may hold Wyner–Ziv side information (Y′, Y″) and share common randomness U; the decoder outputs Ŝ. Two constraints: expected distortion E d(Sⁿ, Ŝⁿ) ≤ D, and a perception constraint, the total variation between the laws of S and Ŝ, either per block (“strong”) or on expectations (“empirical”).
  • The region (Definition 3, Theorem 1). Rate R ≥ I(X; Z|Y), with I(S, X; Z|Y) ≤ (k/m) I(M; M̂) for the channel, Z depending on X only; claimed achievable and tight, by a strong-functional-representation code. The proof is a sketch.
  • Binary case (Theorem 2). For a doubly symmetric binary pair with crossover q, the distortion on S is linear in the distortion on X, d(S, Ŝ) = (1 − 2q) d(X, Ŝ) + q, so reproducing the observation exactly still leaves distortion q on the semantic source (Observation 3); and when the tolerated distortion reaches the level achievable from the side information, the rate is zero (Observation 5).
  • Illustration (Section V). On MNIST with additive noise, a learned encoder and decoder trained on MSE plus a Wasserstein penalty: side information at the decoder lowers the rate at given distortion and perception, and indirect observation raises it.

Standing in the record

Filed on 2026-10-09 from the manuscript bibliography of 2026-10-09 (work what-survives-translation) at the owner’s request. It is the “Chai et al.” the exchange named when it conceded that task-sensitive information preservation is established in semantic communication (CLAIM-088); the manuscript did not keep it. It is read here on its own merits. See the curation entry of that day.

The reading supports the concession in a specific form: preserving a hidden variable S rather than the observation, with decoder side information and a distributional constraint, is formalised here. What is preserved is a single latent variable and its marginal law, not a family of decisions or a distribution over interpretations. Zhao et al. (LIT-793) cite it and move the constraint to the posterior p(S|·). With the survey (LIT-823) it is a source of THEORY-161.

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