Applied Functional Analysis related to Mathematical Information Theory

与数学信息论相关的应用泛函分析

• 批准号: 11640169
• 负责人: YANAGI Kenjiro
• 金额: $ 2.3万
• 依托单位: YAMAGUCHI UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640169/
• 关键词: Information Theory; Gaussian Channel; Capacity; Feedback; Gaussian Noise; Upper Bound; Avcrage Power Constraint; Shannaon Theory; 応用函数解析

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 four results on the finite block length capacity of discrete time Gaussian channels with feedback.1. We proved the concavity of feedback capacity C_<n, FB,Z>( ). That is,C_<n, FB,Z>(αP_1+βP_2)【greater than or equal】αC_<n, FB,Z>(P_1)+βC_<n, FB,Z>(P_2).2. We gave the useful upper bound to blockwise white feedback capacity C_<n, FB,Z>(P) when the power constraint P is relatively large. That is, for any P>P_0={mr_m-(r_1+r_2+…+r_m)}/n,C_<n, FB,Z>(P)【less than or equal】(C_<n, Z>(P))/(P_0)P,C_<n, FB,Z>(P)【less than or equal】C_<n, Z>(P_0)+1/2logP/(P_0).3. We gave the operator convexity of log(1+t^<-1>). As its application we proved the convexity of nonfeedback capacity C_n, .(P). That is,C_<n, Z>(P)【less than or equal】αC_<n, Z_1>(P)+βC_<n, Z_2>(P).4. We proved the convex-likeness of feedback capacity C_<n, FB,>.(P). That is, there exist P_1, P_2【greater than or equal】0(P=αP_1+βP_2) such thatC_<n, FB,Z>(P)【less than or equal】αC_<n, FB,Z_1>(P_1)+βC_<n, FB,Z_2>(P_2).In future we will try to prove the convexity of feedback capacity.

数学信息论最初是由C.E.香农于1948年创立的。从那时起，它发展了数学基础，使通信系统确定。在这项研究中，我们有四个结果的有限块长度容量的离散时间高斯信道的反馈.本文证明了反馈容量C_（n，FB，Z）的稳定性。即C_<n，FB，Z>（αP_1+βP_2）≥ αC_<n，FB，Z>（P_1）+βC_<n，FB，Z>（P_2）。当功率约束P较大时，给出了块式白色反馈容量C_n，FB，Z>（P）的有用上界。即对任意P>P_0={mr_m-（r_1+r_2+.+r_m）}/n，C_n，FB，Z>（P）[小于或等于]（C_n，Z>（P））/（P_0）P，C_n，FB，Z>（P）[小于或等于]C_n，Z>（P_0）+1/2logP/（P_0）。给出了log（1+t^）的算子凸性<-1>.作为其应用，我们证明了无反馈容量C_n，.（P）.即C_（n，Z）（P）≤ αC_（n，Z）（P）+βC_（n，Z）（P）。证明了反馈容量C_&lt;n，FB，&gt;的类凸性。（P）.即存在P_1，P_2[大于或等于]0（P=αP_1+βP_2）使得C_&lt;n，FB，Z&gt;（P）[小于或等于]αC_&lt;n，FB，Z_1&gt;（P_1）+βC_&lt;n，FB，Z_2&gt;（P_2）.

项目成果

陳漢武: "ガウス型通信路容量に関する不等式"京都大学数理解析研究所講究録. 1100. 117-130 (1999)

陈汉武：《关于高斯通道容量的不等式》京都大学数学科学研究所讲座记录。1100. 117-130 (1999)。

Han Wu Chen: "Refinements of the half-bit and factor-of-two bounds for capacity in Gaussian channel with feedback"IEEE Trans.Information Theory. vol.IT-45, no.1. 319-325 (1999)

陈汉武：“带反馈的高斯信道容量的半比特和二倍数界限的改进”IEEE Trans.Information Theory。

Han Wu Chen: "Upper bounds on the capacity of discrete time blockwise white Gaussian channel with feedback"IEEE Transaction on Information Theory. (to appear).

陈汉武：“带反馈的离散时间分块白高斯通道容量的上限”IEEE信息论汇刊。

Kenjiro Yanagi: "Operator inequality and its application to capacity of Gaussian channel"Taiwanese J.Math.. vol.4, no.3. 407-416 (2000)

Kenjiro Yanagi：“算子不等式及其在高斯通道容量中的应用”台湾数学杂志第4卷第3期。

柳 研二郎: "作用素不等式の情報理論への応用"実解析シンポジウム報告集. 58-67 (1999)

Kenjiro Yanagi：“算子不等式在信息论中的应用”实分析研讨会报告 58-67 (1999)。