2013/09/29 by Masahito Hayashi, Shun Watanabe, Hayashi, Masahito +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · #Cooperative Communication and Network Coding #DNA and Biological Computing #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1309.7528
51 pages; 2 figures; presented at Allerton 2013 and ITA 2014; v2 fixed a gap in Remark 5; v3 changed the organization and presentation of the paper; Sections 2 and 3 in v2 were removed in v3, and extended version of them are in separate papers (cf. arXiv:1401.3801 and arXiv:1401.3814); in v4, results on random number generation are removed, and will appear in a separate paper
openalex publication_date 2013/09/29 · arxiv created 2017/01/09 · arxiv updated 2017/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study finite-length bounds for source coding with side information for Markov sources and channel coding for channels with conditional Markovian additive noise. For this purpose, we propose two criteria for finite-length bounds. One is the asymptotic optimality and the other is the efficient computability of the bound. Then, we derive finite-length upper and lower bounds for coding length in both settings so that their computational complexity is efficient. To discuss the first criterion, we derive the large deviation bounds, the moderate deviation bounds, and second order bounds for these two topics, and show that these finite-length bounds achieves the asymptotic optimality in these senses. For this discussion, we introduce several kinds of information measure for transition matrices.