Reduction of Sufficient Number of Code Tables of $k$-Bit Delay Decodable Codes
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914953492955136 |
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| author | Hashimoto, Kengo Iwata, Ken-ichi |
| author_facet | Hashimoto, Kengo Iwata, Ken-ichi |
| contents | A $k$-bit delay decodable code-tuple is a lossless source code that can achieve a smaller average codeword length than Huffman codes by using a finite number of code tables and allowing at most $k$-bit delay for decoding. It is known that there exists a $k$-bit delay decodable code-tuple with at most $2^{(2^k)}$ code tables that attains the optimal average codeword length among all the $k$-bit delay decodable code-tuples for any given i.i.d. source distribution. Namely, it suffices to consider only the code-tuples with at most $2^{(2^k)}$ code tables to accomplish optimality. In this paper, we propose a method to dramatically reduce the number of code tables to be considered in the theoretical analysis, code construction, and coding process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13287 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reduction of Sufficient Number of Code Tables of $k$-Bit Delay Decodable Codes Hashimoto, Kengo Iwata, Ken-ichi Information Theory A $k$-bit delay decodable code-tuple is a lossless source code that can achieve a smaller average codeword length than Huffman codes by using a finite number of code tables and allowing at most $k$-bit delay for decoding. It is known that there exists a $k$-bit delay decodable code-tuple with at most $2^{(2^k)}$ code tables that attains the optimal average codeword length among all the $k$-bit delay decodable code-tuples for any given i.i.d. source distribution. Namely, it suffices to consider only the code-tuples with at most $2^{(2^k)}$ code tables to accomplish optimality. In this paper, we propose a method to dramatically reduce the number of code tables to be considered in the theoretical analysis, code construction, and coding process. |
| title | Reduction of Sufficient Number of Code Tables of $k$-Bit Delay Decodable Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2409.13287 |