2018/01/13 by Hideki Yagi, Yagi, Hideki, Te Sun Han +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Algorithms and Data Compression #DNA and Biological Computing #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.1801.04439
openalex publication_date 2018/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the problem of variable-length δ-channel resolvability, the channel output is approximated by encoding a variable-length uniform random number under the constraint that the variational distance between the target and approximated distributions should be within a given constant δ asymptotically. In this paper, we assume that the given channel input is a mixed source whose components may be general sources. To analyze the minimum achievable length rate of the uniform random number, called the δ-resolvability, we introduce a variant problem of the variable-length δ-channel resolvability. A general formula for the δ-resolvability in this variant problem is established for a general channel. When the channel is an identity mapping, it is shown that the δ-resolvability in the original and variant problems coincide. This relation leads to a direct derivation of a single-letter formula for the δ-resolvability when the given source is a mixed memoryless source. We extend the result to the second-order case. As a byproduct, we obtain the first-order and second-order formulas for fixed-to-variable length source coding allowing error probability up to δ.