Gangtao Xin, Pingyi Fan and Khaled B. Letaief (2024), Entropy 26(2):102 — DOI-10.3390/e26020102
Key takeaways
- The frame (Section 1). Weaver’s three levels: technical (are the symbols received?), semantic (is the intended meaning conveyed?), effectiveness (does it change conduct as desired?). Semantic communication is the second; Shannon’s theory serves the first and ignores truth, task relevance and timeliness.
- Semantic entropy has no agreed definition (Section 3). Carnap and Bar-Hillel’s H_s(e) = −log m(e), with m(e) a logical probability, gives a contradiction infinite information; Floridi and D’Alfonso measure distance from truth instead; Bao et al. weight models of a sentence by their statistical probability. Later variants are task-oriented (the least expected number of queries needed to solve a task), knowledge-based (entropy relative to a knowledge base) or context-based (outcomes weighted by their utility for a goal).
- Semantic rate–distortion is the most developed part (Section 4). In Liu, Zhang and Poor’s framework the source is a pair (S, X): S the unobservable intrinsic state (the “semantic” aspect), X the observation; the encoder sees only X, and the rate is traded against a semantic distortion on S and an appearance distortion on X. Extensions add side information at the decoder (Guo et al.) and Hamming distortion (Stavrou and Kountouris).
- Semantic capacity can exceed channel capacity, by definition (Section 5). Bao et al.’s semantic channel coding theorem adds a term for the receiver’s inferential power and subtracts one for encoding ambiguity; Ma et al. divide Shannon capacity by the fraction of messages that carry distinct meanings. Either way, a system may tolerate bit errors without semantic error. The authors’ own view is that a general semantic capacity must be conditioned on task, shared and private knowledge, goals and time.
- Tools, not theory (Section 6): age of information and its semantics-aware variants, the information bottleneck, deep joint source–channel coding (DeepSC and its successors), and LLMs as knowledge bases.
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 survey the
exchange named when it conceded that task-sensitive information
preservation is established in semantic and goal-oriented 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 finds that the survey supports the concession in general terms (task-relative and goal-oriented formulations are a recognised line of work) but does not cover the rate–distortion–perception results the exchange named alongside it, Chai et al. (LIT-812) and Zhao et al. (LIT-793). Its section on the information bottleneck cites Tishby, Pereira and Bialek’s bottleneck, LIT-338, and Zaslavsky, Kemp, Regier and Tishby’s short paper on human-like semantic representations (arXiv 1808.03353), not the colour-naming paper held here as LIT-810, whose finding it reports. The record’s account of what the semantic rate–distortion frameworks formalise is THEORY-161.