Applied Functional Analysis related to Mathematical Information Theory

数学信息论最初是由c.e.香农于1948年创立的。在本研究中，我们得到了五个关于具有反馈的离散时间高斯信道的有限块长容量的结果。给出了功率约束P较大时反馈容量C_<n， FB> (P)的有用上界。给出了当功率约束P较小时反馈容量C_<n， FB> (P)的有用上界。我们改进了Cover和Pombra在1989年给出的反馈能力的上界。也就是说，对于任意b> 0和任意p> 0 4。我们解决了1987年Cover在n = 2的情况下给出的关于反馈容量的猜想。也就是说,5。给出了反馈容量的一些自不等式，这些不等式可以应用于带反馈的块状高斯白信道的容量上界。即对于任意0 < alpha < <小于等于> 1和任意在未来我们将尝试证明反馈能力的凹性作为功率约束的函数。

The mathematical information theory was originally founded by C.E.Shannon in 1948. Since then, it has developed the mathematical foundations to make the communication systems certain, In this research we have five results on the finite block length capacity of discrete time Gaussian chanAels with feedback.1.We gave the useful upper bound to feedback capacity C_<n, FB> (P) when the power constraint P is relatively large.2.We gave the useful upper bound to feedback capacity C_<n, FB> (P) when the power constraint P is relatively small.3.We refined the upper bound to feedback capacity given by Cover and Pombra in 1989. That is, for any alpha > 0 and any P> 0,4.We solved the conjecture about feedback capacity given by Cover in 1987 in the case of n = 2. That is,5.We gave some self-inequalities of feedback capacity, which can be applied to upper bound to capacity of blockwise white Gaussian channel with feedback. That is, for any 0 < alpha <less than or equal> 1 and anyIn future we will try to prove the concavity of feedback capacity as the function of power constraint.