Abstract and Keywords
This article examines asymptotic singular value distributions in information theory, with particular emphasis on some of the main applications of random matrices to the capacity of communication channels. Results on the spectrum of random matrices have been adopted in information theory. Furthermore, information theorists, motivated by certain channel models, have obtained a number of new results in random matrix theory (RMT). Most of those results are related to the asymptotic distribution of the (square of) the singular values of certain random matrices that model data communication channels. The article first provides an overview of three transforms that are useful in expressing the asymptotic spectrum results — Stieltjes transform, η-transform, and Shannon transform — before discussing the main results on the limit of the empirical distributions of the eigenvalues of various random matrices of interest in information theory.
Keywords: asymptotic distribution, information theory, random matrices, channel model, random matrix theory (RMT), singular value, data communication channel, Stieltjes transform, η-transform, Shannon transform
Access to the complete content on Oxford Handbooks Online requires a subscription or purchase. Public users are able to search the site and view the abstracts and keywords for each book and chapter without a subscription.
If you have purchased a print title that contains an access token, please see the token for information about how to register your code.