2016/09/30 by Anuran Makur, Yury Polyanskiy · 2 citations
Computer Science · Engineering · Mathematics · #Abelian group #Artificial intelligence #Channel (broadcasting) #Characterization (materials science) #Combinatorics #Computer science #Dirichlet distribution #Divergence (linguistics) #Eigenvalues and eigenvectors #Information theory #Kullback–Leibler divergence #Logarithm #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Noise (video) #Physics #Pure mathematics #Random Matrices and Applications #Statistics #Symmetric matrix #Telecommunications #Topology (electrical circuits) #Wireless Communication Security Techniques #cs.IT #math.IT #math.PR #math.ST #stat.TH
paper · pdf · doi:10.1109/tit.2018.2839743
published as IEEE Transactions on Information Theory, vol. 64, no. 8, Aug. 2018 · 31 pages, 2 figures. Presented at 2017 IEEE International Symposium on Information Theory (ISIT)
openalex publication_date 2018/05/23 · arxiv created 2018/12/03 · arxiv updated 2018/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
This paper studies the basic question of whether a given channel V can be dominated (in the precise sense of being more noisy) by a q-ary symmetric channel. The concept of less noisy relation between channels originated in network information theory (broadcast channels) and is defined in terms of mutual information or Kullback-Leibler divergence. We provide an equivalent characterization in terms of χ2-divergence. Furthermore, we develop a simple criterion for domination by a q-ary symmetric channel in terms of the minimum entry of the stochastic matrix defining the channel V. The criterion is strengthened for the special case of additive noise channels over finite Abelian groups. Finally, it is shown that domination by a symmetric channel implies (via comparison of Dirichlet forms) a logarithmic Sobolev inequality for the original channel.