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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/2604.17443 |
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| _version_ | 1866917420607733760 |
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| author | Liu, Hongyang Yan, Wei |
| author_facet | Liu, Hongyang Yan, Wei |
| contents | For the discrete memoryless sources with a countably infinite alphabet, we prove that for any positive integer $k$, there exists a corresponding probability interval such that if the largest symbol probability $p_{1}$ falls in this interval, the optimal code length for the symbol equals $k$. Furthermore, for infinite sources, we provide a criterion to determine probability distributions whose optimal code length assignment follows the pattern $l^{best}_{i}=i$, for $i\ge 1$. Compared with the existing conclusion for anti-uniform sources, the proposed criterion requires less information for verification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17443 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | About Optimal Prefix Codes over Countably Infinite Alphabets: Probabilistic Intervals for the Codeword Lengths Assignment Liu, Hongyang Yan, Wei Information Theory For the discrete memoryless sources with a countably infinite alphabet, we prove that for any positive integer $k$, there exists a corresponding probability interval such that if the largest symbol probability $p_{1}$ falls in this interval, the optimal code length for the symbol equals $k$. Furthermore, for infinite sources, we provide a criterion to determine probability distributions whose optimal code length assignment follows the pattern $l^{best}_{i}=i$, for $i\ge 1$. Compared with the existing conclusion for anti-uniform sources, the proposed criterion requires less information for verification. |
| title | About Optimal Prefix Codes over Countably Infinite Alphabets: Probabilistic Intervals for the Codeword Lengths Assignment |
| topic | Information Theory |
| url | https://arxiv.org/abs/2604.17443 |