# American Institute of Mathematical Sciences

September  2007, 6(3): 819-827. doi: 10.3934/cpaa.2007.6.819

## Localization operator and digital communication capacity of channel

 1 LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China, China, China

Received  May 2005 Revised  August 2006 Published  June 2007

In mathematical language, the communication model of some digital information channel can be described as the self-adjoint operator $Q_T P_\Omega Q_T$ on $L^2(R)$, where $T$ and $\Omega$ are constants. $T$ is called signal peroid and $\Omega$ is called channel's bandwidth. By computing the eigenvalues and the corresponding eigenfunctions of the compact self-adjoint operator $Q_T P_\Omega Q_T$, the conclusion of Landau, Pollak and Slepian shows that about $2\Omega T$ bits data can be transmitted by this channel within time $T$ when $\Omega T$ is sufficiently large. Considering the realistic communication model, this paper points out that in one signal period $T$, at most $2r\Omega T$ can be transmitted with $r$ ($r\in (0,1)$) dependent on some given threshold $\eta$.
Citation: Lizhong Peng, Shujun Dang, Bojin Zhuang. Localization operator and digital communication capacity of channel. Communications on Pure & Applied Analysis, 2007, 6 (3) : 819-827. doi: 10.3934/cpaa.2007.6.819
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