Exact Redundancy for Symmetric Rate-Distortion
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912829955637248 |
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| author | Sriramu, Sharang M. Wagner, Aaron B. |
| author_facet | Sriramu, Sharang M. Wagner, Aaron B. |
| contents | For variable-length coding with an almost-sure distortion constraint, Zhang et al. show that for discrete sources the redundancy is upper bounded by $\log n/n$ and lower bounded (in most cases) by $\log n/(2n)$, ignoring lower order terms. For a uniform source with a distortion measure satisfying certain symmetry conditions, we show that $\log n/(2n)$ is achievable and that this cannot be improved even if one relaxes the distortion constraint to be in expectation rather than with probability one. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_11927 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact Redundancy for Symmetric Rate-Distortion Sriramu, Sharang M. Wagner, Aaron B. Information Theory For variable-length coding with an almost-sure distortion constraint, Zhang et al. show that for discrete sources the redundancy is upper bounded by $\log n/n$ and lower bounded (in most cases) by $\log n/(2n)$, ignoring lower order terms. For a uniform source with a distortion measure satisfying certain symmetry conditions, we show that $\log n/(2n)$ is achievable and that this cannot be improved even if one relaxes the distortion constraint to be in expectation rather than with probability one. |
| title | Exact Redundancy for Symmetric Rate-Distortion |
| topic | Information Theory |
| url | https://arxiv.org/abs/2601.11927 |