1、信息論實(shí)驗(yàn)報(bào)告任務(wù)一一、實(shí)驗(yàn)要求：擲兩個(gè)骰子（各面出現(xiàn)概率相同）O理論計(jì)算：各個(gè)加和出現(xiàn)的概率T熵O仿真：仿真完成擲轂子游戲T統(tǒng)計(jì)概率T計(jì)算熵O取不同的N值，比較理論和仿真結(jié)果二、實(shí)驗(yàn)內(nèi)容1、理論計(jì)算點(diǎn)數(shù)234567概率1/362/363/364/365/366/36點(diǎn)數(shù)89101112概率5/364/363/362/361/36熵H=2.272、仿真實(shí)驗(yàn)次數(shù)n=360次時(shí):hanewark0.0222D.D5D00.06390.1333Q.11940.18330.150D0.D94-4-0-07500.D0330.025D實(shí)驗(yàn)次數(shù)n=3600次時(shí):Q.02350.Call0.085S0.11

2、750.14030.1639D.14500.1L14003690.0475O.QZS2.2537實(shí)驗(yàn)次數(shù)n=36000次時(shí)：hoDvork0.02800.05580.08300.11180.13B00.16550.1384山11130,08370,05630,0575h=2-2709由仿真結(jié)果可知，隨著n值的增大，仿真結(jié)果趨于接近理論值。3、源代碼實(shí)驗(yàn)源代碼n=360000;data1=6*rand(1,n)+0.5;data2=6*rand(1,n)+0.5;y1=round(data1);y2=round(data2);y=y1+y2;num=zeros(1,11);fori=1:nswi

3、tchy(i)case2num(1)=num(1)+1;case3num(2)=num(2)+1;case4num(3)=num(3)+1;case5num(4)=num(4)+1;case6num(5)=num(5)+1;case7num(6)=num(6)+1;case8num(7)=num(7)+1;case9num(8)=num(8)+1;case10num(9)=num(9)+1;case11num(10)=num(10)+1;otherwisenum(11)=num(11)+1;endendp=num/n;h=0;fori=1:11h=h-p(i)*log(p(i);endh任務(wù)二

4、一、實(shí)驗(yàn)要求：二進(jìn)制對(duì)稱信道(BSC)的互信息：O二進(jìn)制信源0,1,PX(0)=0.5。條件概率：PY|X(0|0)=PY|X(l|l)=l-p,PY|X(l|0)=PY|X(0|1)=p。O計(jì)算I(X;Y),并繪制I(X;Y)與p的關(guān)系曲線。O生成長(zhǎng)度為N的二進(jìn)制信源作為輸入X,輸出為Y。統(tǒng)計(jì)X和Y之間的“差錯(cuò)率”討論差錯(cuò)率與I(X;Y)的關(guān)系。二、實(shí)驗(yàn)內(nèi)容：1-I(X;Y)與p的關(guān)系曲線2-差錯(cuò)率與I(X;Y)的關(guān)系曲線測(cè)試長(zhǎng)度N=1000時(shí)。nJH5B已D.60.70.80.90.10.20.3Q4S4tEl荼蘭芝切捲入山I3CD疵3LIM逋口凹）ffih3.差錯(cuò)率與p的關(guān)系曲線D.90

5、.80.70.6D.320.1a.2QJ0.40.50.6o.zO.S09刁已R給池|亀亀巴渥尿J屈困口交件舊環(huán)2）室JSA01工勲門寶血琶口務(wù)或陽）p=0.01*i;px=0.5,0.5;pxy=1-p,p;p,1-p;py=px*pxy;hy(i)=-(py(1)*log(py(1)+py(2)*log(py(2);三、源代碼fori=1:100hyx(i)=-py(1)*(pxy(1,1)*log(pxy(1,1)+pxy(1,2)*log(pxy(1,2)-py(2)*(pxy(2,1)*log(pxy(2,1)+pxy(2,2)*log(pxy(2,2);ixy(i)=hy(i)-h

6、yx(i);end%pp=0.01:0.01:1;%plot(pp,ixy);n=100;N=1000;x=round(rand(1,N);count=zeros(1,n);forj=1:np=j/n;pxy=1-p,p;p,1-p;fori=1:Nif(x(i)=0)if(rand(1)pxy(1,1)y(i)=0;elsey(i)=1;endelseif(x(i)=1)if(rand(1)pxy(2,1)y(i)=0;elsey(i)=1;endendif(x(i)=y(i)count(j)=count(j)+1;endendendpp=0.01:0.01:1;%plot(pp,count

7、/N);%plot(count/N,ixy);可選任務(wù)一一、實(shí)驗(yàn)要求：計(jì)算英文文本的熵O導(dǎo)入一定長(zhǎng)度的英文文本O統(tǒng)計(jì)每個(gè)字母出現(xiàn)的概率T計(jì)算熵H(X)O統(tǒng)計(jì)每?jī)蓚€(gè)字母出現(xiàn)的概率T計(jì)算熵h(x2|xi)O比較H(X)和H(X2|X1)，并對(duì)結(jié)果進(jìn)行討論二、實(shí)驗(yàn)內(nèi)容測(cè)試數(shù)據(jù)為：data=ThisisthefirsttimethatChinahoststheworldsmostinfluentialbiannualquantumconferencewhichwilllastuntilThursdayThebasicpremiseofthetheoryisthatwealwayshavesomepre

8、liminaryknowledgeabouttheoccurrenceofeventsthatarerelevanttoourdecisionsTheimportanceofaccuratedatavarieswiththetypeofdecisionsthatneedtobemade;計(jì)算其熵H(x)計(jì)算結(jié)果如圖所示：命術(shù)匚F匸dliAHJ1Lhfgh】百E.7077n.03351.333B1.WOO山陰8厲ML30.?077hfJLBD.2M5ZD.OIBDi山珂眈山羽擁0.038&0.J41&D.107T0.A3E3CalmrL17thrcuh.2?0.730g0.O.OJ330.6L&

9、40.74Q21.234B0.3-180.Li3&D.芻裁D.L22M0.L酸M該段無記憶信源的熵為3.0379三、實(shí)驗(yàn)代碼data=ThisisthefirsttimethatChinahoststheworldsmostinfluentialbiannualquantumconferencewhichwilllastuntilThursdayThebasicpremiseofthetheoryisthatwealwayshavesomepreliminaryknowledgeabouttheoccurrenceofeventsthatarerelevanttoourdecisionsTheimportanceofaccuratedatavarieswiththetypeofdecisionsthatneedtobemade;%任意字符串%data=aeabebbcecccddedde%測(cè)試串a(chǎn)=unique