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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.09113 |
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| _version_ | 1866917518822604800 |
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| author | Mishra, Prachi Jaggi, Sidharth Kashyap, Navin Langberg, Michael |
| author_facet | Mishra, Prachi Jaggi, Sidharth Kashyap, Navin Langberg, Michael |
| contents | We investigate weakly constrained codes, in which specific patterns occur with prescribed frequencies rather than being strictly forbidden as in conventional constrained coding. We propose a capacity-achieving construction of a weakly constrained codebook based on Eulerian cycles. We then obtain, via expurgation, weakly constrained codes with linear minimum distance and positive rate, and analyze the rates achievable. Finally, we propose a practical concatenated code construction that supports polynomial-time encoding and decoding. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09113 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Error-Correcting Weakly Constrained Codes: Constructions and Achievable Rates Mishra, Prachi Jaggi, Sidharth Kashyap, Navin Langberg, Michael Information Theory We investigate weakly constrained codes, in which specific patterns occur with prescribed frequencies rather than being strictly forbidden as in conventional constrained coding. We propose a capacity-achieving construction of a weakly constrained codebook based on Eulerian cycles. We then obtain, via expurgation, weakly constrained codes with linear minimum distance and positive rate, and analyze the rates achievable. Finally, we propose a practical concatenated code construction that supports polynomial-time encoding and decoding. |
| title | Error-Correcting Weakly Constrained Codes: Constructions and Achievable Rates |
| topic | Information Theory |
| url | https://arxiv.org/abs/2605.09113 |