Reduction of Sufficient Number of Code Tables of $k$-Bit Delay Decodable Codes
<|reference_start|>Reduction of Sufficient Number of Code Tables of $k$-Bit Delay Decodable Codes: 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.<|reference_end|>
@article{hashimoto2024reduction,
    title={Reduction of Sufficient Number of Code Tables of $k$-Bit Delay Decodable
  Codes},
    author={Kengo Hashimoto, Ken-ichi Iwata},
    journal={arXiv preprint arXiv:2409.13287},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.13287},
    primaryClass={cs.IT math.IT}
}