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Semantic Arithmetic Coding using Synonymous Mappings

Zijian Liang, Kai Niu, Jin Xu, Ping Zhang

TL;DR

This work introduces semantic arithmetic coding (SAC), a semantic-source-coding framework that uses carefully designed synonymous mappings to partition semantic information into synonymous sets and perform arithmetic coding over those sets. By tying semantic content to synonymous structures, SAC achieves compression near the semantic entropy $H_s(\tilde{\mathcal{U}})$ while preserving meaning, demonstrated through an edge texture map experiment where semantic integrity is maintained and compression improves over conventional arithmetic coding. The authors extend the code-length theorem to the semantic domain, showing that the average code length can approach $H_s(\tilde{\mathcal{U}})$ as the sequence length grows, and provide empirical evidence of lossless semantic reconstruction with meaningful reductions in bits. Overall, SAC offers a principled approach to semantic lossless compression with theoretically grounded limits and practical effectiveness for semantics-rich sources.

Abstract

Recent semantic communication methods explore effective ways to expand the communication paradigm and improve the system performance of the communication systems. Nonetheless, the common problem of these methods is that the essence of semantics is not explicitly pointed out and directly utilized. A new epistemology suggests that synonymy, which is revealed as the fundamental feature of semantics, guides the establishment of the semantic information theory from a novel viewpoint. Building on this theoretical basis, this paper proposes a semantic arithmetic coding (SAC) method for semantic lossless compression using intuitive semantic synonymy. By constructing reasonable synonymous mappings and performing arithmetic coding procedures over synonymous sets, SAC can achieve higher compression efficiency for meaning-contained source sequences at the semantic level and thereby approximate the semantic entropy limits. Experimental results on edge texture map compression show an evident improvement in coding efficiency using SAC without semantic losses, compared to traditional arithmetic coding, which demonstrates its effectiveness.

Semantic Arithmetic Coding using Synonymous Mappings

TL;DR

This work introduces semantic arithmetic coding (SAC), a semantic-source-coding framework that uses carefully designed synonymous mappings to partition semantic information into synonymous sets and perform arithmetic coding over those sets. By tying semantic content to synonymous structures, SAC achieves compression near the semantic entropy while preserving meaning, demonstrated through an edge texture map experiment where semantic integrity is maintained and compression improves over conventional arithmetic coding. The authors extend the code-length theorem to the semantic domain, showing that the average code length can approach as the sequence length grows, and provide empirical evidence of lossless semantic reconstruction with meaningful reductions in bits. Overall, SAC offers a principled approach to semantic lossless compression with theoretically grounded limits and practical effectiveness for semantics-rich sources.

Abstract

Recent semantic communication methods explore effective ways to expand the communication paradigm and improve the system performance of the communication systems. Nonetheless, the common problem of these methods is that the essence of semantics is not explicitly pointed out and directly utilized. A new epistemology suggests that synonymy, which is revealed as the fundamental feature of semantics, guides the establishment of the semantic information theory from a novel viewpoint. Building on this theoretical basis, this paper proposes a semantic arithmetic coding (SAC) method for semantic lossless compression using intuitive semantic synonymy. By constructing reasonable synonymous mappings and performing arithmetic coding procedures over synonymous sets, SAC can achieve higher compression efficiency for meaning-contained source sequences at the semantic level and thereby approximate the semantic entropy limits. Experimental results on edge texture map compression show an evident improvement in coding efficiency using SAC without semantic losses, compared to traditional arithmetic coding, which demonstrates its effectiveness.
Paper Structure (10 sections, 1 theorem, 5 equations, 4 figures, 2 algorithms)

This paper contains 10 sections, 1 theorem, 5 equations, 4 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model and Theoretical Limits
  3. System Model
  4. Synonymous Mappings-based Theoretical Limits
  5. Semantic Arithmetic Codes
  6. The Encoding Procedure
  7. The Decoding Procedure
  8. Theoretical Limits Analysis
  9. Experimental Results
  10. Conclusion

Key Result

Theorem 1

For a semantic arithmetic coding procedure, given any syntactic sequence ${u}^m$ with the probability mass function of its corresponding synonymous set sequence $q\left(\mathcal{U}_{1,r_1},\ldots,\mathcal{U}_{m,r_m}\right)$, it enables one to encode ${u}^m$ in a code of length $-\log q\left(\mathcal

Figures (4)

  • Figure 1: An example of the synonymous mappings and the corresponding synonymous sets.
  • Figure 2: A schematic diagram of the SAC encoding procedure.
  • Figure 3: The synonymous sets partition for edge texture maps.
  • Figure 4: An example of the compression and the reconstruction effects for edge texture map semantic compression, in which "sebits" denotes semantic bits for the resulting unit of semantic source coding, presented by niu2024Mathematical. Besides, "bit/pb" and "sebit/pb" respectively denote bit per pixel block and sebit per pixel block, acting as the unit of the entropy and the average code length of traditional AC and our proposed SAC based on our coding configuration.

Theorems & Definitions (1)

  • Theorem 1