二元对称信道平均互信息的图形分析信息论与编码实验报告.docx
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二元对称信道平均互信息的图形分析信息论与编码实验报告.docx
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二元对称信道平均互信息的图形分析信息论与编码实验报告
二元对称信道平均互信息的图形分析-信息论与编码实验报告
计算机与信息工程学院设计性实验报告
专业:
通信工程年级/班级:
2011级2013—2014学年第一学期课程名称信息论与编码指导教师刘艳芳本组成员1108224020李明亮学号姓名
实验地点计科楼111实验时间周五5-6节
二元对称信道平均互信息的图形分析项目名称实验类型设计性
一、实验目的
分别画出在给定条件下,平均互信息的上凸性和下凸性的图形,然后利用计算机仿真二元对称信道,观察改变变量w或p时,所绘图形的变化情况。
二、实验仪器或设备
1、一台计算机。
2、MATLABr2013a。
三、设计原理
设二元对称信道的输入概率空间:
01,,X,,,,,,,Ppp,,,,
信道矩阵:
,,,,.P,,,
,,,,,
其中:
1
pbpapbapp(0)()(|),,,,,,,ii0,i0
1
pbpapbapp
(1)()(|),,,,,,,ii1,i0
11HYppppHpp,,,,,,,,,,,,()()log()log()pppp,,,,,,
HYXpapbapba(|)()(|)log(|),,,,ijijiij
,pbapba(|)log(|),jijij
,,,,,,[loglog]
H(),
real,ineachpenbusinesslendingQiannotforbypenquery,ledtomortgagefailureof.(Vi)notinaccordancewiththerelevantprovisionsoftheBankoperation,failedtoidentifyfalsedocuments,certificates,authorizations,warrants,etc.(VII)inthecreditriskmanagementsystemtoprovidefalseinformation,isnotrequiredbytheguestratingcreditmanagementobjective,impartialratingsofcredit,resultingincreditdecision-makingerrors.(H)theinvestigationreportconclusionsoffalserecord,misleadingstatementormaterialomission,resultingincreditdecision-makingerrors.(I)theorders,directives,orders,suggestthatothersnotinvolvedintheinvestigationbusiness,issuedbytheinvestigators.(10)withouttheapprovalofauthorities,afterthefirstcreditinvestigation,creditfirstandthenrecord,counter-currentprocessoperationssuchasoperationpriortoapproval.(11)articledoesnotmeettheriskmanagementDepartment,MarketingManagementDepartmenttocarryoutsupervisionandinspectionandduediligenceevaluationsorprovidingfalseinformation.(12)otherviolationsresultincreditbusinessatsubstantialriskorsignificantpotentialriskbehaviours.Sixthchaptersupplementaryarticlesarticle28thofthisapproachbytheHeadOfficeofriskmanagementDepartmentisresponsiblefortheinterpretationandamendment.29thspontaneoushereinfromthedateofimplementation.QilusilvercomputertransmissionofqiluBankdocuments(2012),No.289QiluBankpersonalcreditonissuingtheNotificationGuidetobusinessriskmanagementbranch,jurisdictionandthejurisdictionofbusinesslines,Jinanbranch,headofficedepartmentswithinitsjurisdiction:
inordertoimprovethequalityofindividualcreditbusiness,optimizethestructureofassets,promotionof
IXYHYHYXHppH(;)()(|)()(),,,,,,,,
四、实验步骤
(1)试验程序,依次输出题目要求的三个图形
%信源w固定,当w=0.5时,互信息随信道转移概率P的变化情况figure
(1)
w=0.5;%信源w=0.5
p=0:
.01:
1;%信道不固定,在0~1变化
IXY=ESC2H(w.*(1-p)+(1-w).*p)-ESC2H(p);
plot(p,IXY);
title('信源w=0.5时,互信息随信道转移概率P的变化情况')xlabel('p')
ylabel('互信息IXY')
%信道P固定,当P取值不是0.5,互信息随信源w的变化情况figure
(2)
p=0.3;%信道P固定,取值不是0.5
w=0:
.01:
1;%信原不固定,在0~1变化
IXY=ESC2H(w.*(1-p)+(1-w).*p)-ESC2H(p);
plot(w,IXY)
title('信道P=0.3时(不为0.5),互信息随信源w的变化情况')xlabel('w')
ylabel('互信息IXY')
%信道P固定,当p=0.5,互信息随信源w的变化情况
figure(3)
p=0.5;%信道P固定,取值不是0.5
w=0:
.01:
1;%信原不固定,在0~1变化
IXY=ESC2H(w.*(1-p)+(1-w).*p)-ESC2H(p);
plot(w,IXY)
title('信道P=0.5,互信息随信源w的变化情况')xlabel('w')
ylabel('互信息IXY')
(2)ESC2H.m:
%简单求二元熵函数
function[l_ans]=ESC2H(l_input)%[l_ans]=ESC2H(l_input)%输入:
二元信源(信道),其中一元的概率
%输出:
二元熵
ifl_input>1|l_input<0
error('输入值有误,其值超出了概率范围')
else
l_find=[find(l_input==0),find(l_input==1)];
l_input(l_find)=0.5;
real,ineachpenbusinesslendingQiannotforbypenquery,ledtomortgagefailureof.(Vi)notinaccordancewiththerelevantprovisionsoftheBankoperation,failedtoidentifyfalsedocuments,certificates,authorizations,warrants,etc.(VII)inthecreditriskmanagementsystemtoprovidefalseinformation,isnotrequiredbytheguestratingcreditmanagementobjective,impartialratingsofcredit,resultingincreditdecision-makingerrors.(H)theinvestigationreportconclusionsoffalserecord,misleadingstatementormaterialomission,resultingincreditdecision-makingerrors.(I)theorders,directives,orders,suggestthatothersnotinvolvedintheinvestigationbusiness,issuedbytheinvestigators.(10)withouttheapprovalofauthorities,afterthefirstcreditinvestigation,creditfirstandthenrecord,counter-currentprocessoperationssuchasoperationpriortoapproval.(11)articledoesnotmeettheriskmanagementDepartment,MarketingManagementDepartmenttocarryoutsupervisionandinspectionandduediligenceevaluationsorprovidingfalseinformation.(12)otherviolationsresultincreditbusinessatsubstantialriskorsignificantpotentialriskbehaviours.Sixthchaptersupplementaryarticlesarticle28thofthisapproachbytheHeadOfficeofriskmanagementDepartmentisresponsiblefortheinterpretationandamendment.29thspontaneoushereinfromthedateofimplementation.QilusilvercomputertransmissionofqiluBankdocuments(2012),No.289QiluBankpersonalcreditonissuingtheNotificationGuidetobusinessriskmanagementbranch,jurisdictionandthejurisdictionofbusinesslines,Jinanbranch,headofficedepartmentswithinitsjurisdiction:
inordertoimprovethequalityofindividualcreditbusiness,optimizethestructureofassets,promotionof
l_ans=-l_input.*log2(l_input)-(1-l_input).*log2((1-l_input));
l_ans(l_find)=0;
end
(3)yanshi.m:
%当取定的数值在0~1变化时,上凸(下凸)函数的变化情况function[m]=yanshi(movie)
%当取定的数值在0~1变化时,上凸(下凸)函数的变化情况
%[m]=yanshi(movie)输入演示序号,输出图形动画及getframe函数产生的电影帧%输入:
movie=1:
演示第一个图形动画
%movie=2:
演示第二个图形动画
%输出:
m:
getframe函数产生的当前动画的电影帧,可使用movie函数进行操作%example:
[m]=yanshi
(1)
%[m]=yanshi
(2)
ifmovie==1
%对于信源w固定,互信息随信道转移概率P的变化图形,
%当w在0~1之间变化时,函数图形的变化情况
%此时,函数图形规律变化
w=0;
fori=1:
100
w=w+0.01;%信源在一帧图形中固定,动画中在0~1变化
p=0:
.01:
1;%信道不固定,在0~1变化
IXY=ESC2H(w.*(1-p)+(1-w).*p)-ESC2H(p);
plot(p,IXY);
axis([-0.11.1-0.11.1])
title('信源W从0到1逐渐变化,具体取值见commandwindow')
xlabel('p')
ylabel('互信息IXY')
m(i)=getframe;
disp(['当前的W取值为',num2str(w)])
end
elseifmovie==2
%对于信道P固定,互信息随信源w的变化图形,
%当p在0~1之间变化时,函数图形的变化情况
%此时,函数图形变化不规律
p=0;
fori=1:
99
p=p+0.01;%信道在一帧图形中固定,动画中在0~1变化
w=0:
.01:
1;%信原不固定,在0~1变化
IXY=ESC2H(w.*(1-p)+(1-w).*p)-ESC2H(p);
plot(w,IXY)
title('信道P从0到1逐渐变化,具体取值见commandwindow')
xlabel('w')
河南师范大学计算机与信息工程学院real,ineachpenbusinesslendingQiannotforbypenquery,ledtomortgagefailureof.(Vi)notinaccordancewiththerelevantprovisionsoftheBankoperation,failedtoidentifyfalsedocuments,certificates,authorizations,warrants,etc.(VII)inthecreditriskmanagementsystemtoprovidefalseinformation,isnotrequiredbytheguestratingcreditmanagementobjective,impartialratingsofcredit,resultingincreditdecision-makingerrors.(H)theinvestigationreportconclusionsoffalserecord,misleadingstatementormaterialomission,resultingincreditdecision-makingerrors.(I)theorders,directives,orders,suggestthatothersnotinvolvedintheinvestigationbusiness,issuedbytheinvestigators.(10)withouttheapprovalofauthorities,afterthefirstcreditinvestigation,creditfirstandthenrecord,counter-currentprocessoperationssuchasoperationpriortoapproval.(11)articledoesnotmeettheriskmanagementDepartment,MarketingManagementDepartmenttocarryoutsupervisionandinspectionandduediligenceevaluationsorprovidingfalseinformation.(12)otherviolationsresultincreditbusinessatsubstantialriskorsignificantpotentialriskbehaviours.Sixthchaptersupplementaryarticlesarticle28thofthisapproachbytheHeadOfficeofriskmanagementDepartmentisresponsiblefortheinterpretationandamendment.29thspontaneoushereinfromthedateofimplementation.QilusilvercomputertransmissionofqiluBankdocuments(2012),No.289QiluBankpersonalcreditonissuingtheNotificationGuidetobusinessriskmanagementbranch,jurisdictionandthejurisdictionofbusinesslines,Jinanbranch,headofficedepartmentswithinitsjurisdiction:
inordertoimprovethequalityofindividualcreditbusiness,optimizethestructureofassets,promotionof
ylabel('互信息IXY')
m(i)=getframe;
disp(['当前的p取值为',num2str(p)])
end
end
end
五、结果分析与总结
(1)程序1输出的图形:
信源w=0.5时,互信息随信道转移概率P的变化情况
1
0.8
0.6
0.4互信息IXY
0.2
000.10.20.30.40.50.60.70.80.91
p
信道P=0.3时(不为0.5),互信息随信源w的变化情况0.12
0.1
0.08
0.06
互信息IXY0.04
0.02
000.10.20.30.40.50.60.70.80.91
w
real,ineachpenbusinesslendingQiannotforbypenquery,ledtomortgagefailureof.(Vi)notinaccordancewiththerelevantprovisionsoftheBankoperation,failedtoidentifyfalsedocuments,certificates,authorizations,warrants,etc.(VII)inthecreditriskmanagementsystemtoprovidefalseinformation,isnotrequiredbytheguestratingcreditmanagementobjective,impartialratingsofcredit,resultingincreditdecision-makingerrors.(H)theinvestigationreportconclusionsoffalserecord,misleadingstatementormaterialomission,resultingincreditdecision-makingerrors.(I)theorders,directives,orders,suggestthatothersnotinvolvedintheinvestigationbusiness,issuedbytheinvestigators.(10)withouttheapprovalofauthorities,afterthefirstcreditinvestigation,creditfirstandthenrecord,counter-currentprocessoperationssuchasoperationpriortoapproval.(11)articledoesnotmeettheriskmanagementDepartment,MarketingManagementDepartmenttocarryoutsupervisionandinspectionandduediligenceevaluationsorprovidingfalseinformation.(12)otherviolationsresultincreditbusinessatsubstantialriskorsignificantpotentialriskbehaviours.Sixthchaptersupplementaryarticlesarticle28thofthisapproachbytheHeadOfficeofriskmanagementDepartmentisresponsiblefortheinterpretationandamendment.29thspontaneoushereinfromthedateofimplementation.QilusilvercomputertransmissionofqiluBankdocuments(2012),No.289QiluBankpersonalcreditonissuin
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- 二元 对称 信道 平均 互信 图形 分析 信息论 编码 实验 报告