信息论第五章 信源编码习题答案

1、-X-厂xxxxxAxx=_P(X)_10.20.190.180.170.150.10.01丿5.1设信源求信源熵H(X);编二进制香农码；计算平均码长和编码效率解：(1)H(X)=-p(x)logp(x)i2ii=1=-(0.2xlog0.2+0.19xlog0.19+0.18xlog0.18+0.17xlog0.172222+0.15xlog0.15+0.1xlog0.1+0.01xlog0.01)222=2.609bit/symbol(2)可用matlab函数dec2bin(a,n)a-小、数，n长度X.p(x)p(x)k码字X0.203000Xo0.190.230012X0.180.3

2、930113X0.170.573100X50.150.743101X60.10.8941110X|710.010.99711111101)0.0-0.0000002)0.2*2=0.400.4*2=0.800.8*2=1.613)0.39*2=0.7800.78*2=1.5610.56*2=1.1214)0.99*2=1.9810.98*2=1.9610.96*2=1.9210.92*2=1.8410.84*2=1.6810.68*2=1.3610.36*2=0.720(3)K=2kp(x)=3x0.2+3x0.19+3x0.18+3x0.17+3x0.15+4x0.1+7x0.01iii=3

3、.14-H(X)=16?=83.1%5.2对信源LP(X)解：x1编二进制费诺码，计算编码效率。0.20.190.180.170.150.10.01X.p(x)X0.2X20.19XO0.183X0.17X0.15X60.1Xq0.01编码码字000100111011011101111ki2丄2丄44p(x)=2x0.2+3x0.19+3x0.18+2x0.17+3x0.15+4x0.1+4x0.01iii=2.74H(X)=HX)=比=95.2%2.74=乩5.3对信源LP(X)自的平均码长和编码效率解：二进制哈夫曼码：x20.19x30.18x40.17x50.15x60.10.01编二进

4、制和三进制哈夫曼码，计算各XP(X.)编码码字ks61s0.610s0.391s0.35030.261X10.20102X20.191112X30.1800003X0.1710013X0.1500103s0.111X0.1001104X0.01101114K=Lkp(x)=2x0.2+2x0.19+3x0.18+3x0.17+3x0.15+4x0.1+4x0.01iii=2.72一警=烂=壽=95.9%三进制哈夫曼码:xp(xi)编码码字ks31s20.540s0.261x0.2221x00.1900022x0.1810123x0.172022x50.150102x0.11112x70.012

5、122K=2kp(x)=lx0.2+2x(0.19+0.18+0.17+0.15+0.1+0.01)ii=1.82.609KlogmL2=91.4%1.8xlog32xxxxxxxxx=V1112131415161718设信源P(X)J、248163264128128J5.4求信源熵H(X);编二进制香农码和二进制费诺码；计算二进制香农码和二进制费诺码的平均码长和编码效率编三进制费诺码；计算三进制费诺码的平均码长和编码效率；解:(1)H(X)=-fp(xi)log2p(xi)i=1=xlog2+xlog4+xlog8+xlog16+xlog32+丄xlog64+-xlog128+-xlog12

6、8224fc28216232264212821282=1.984bit/symbol(2)二进制香农码:X.p(x)p(xJk码字x0.5010 x00.250.52102x30.1250.753110 x40.06250.87541110 x50.031250.9375511110 x610.0156250.9687561111100.00781250.98437571111110 x80.00781250.992187571111111二进制费诺码:xip(xJ编码码字kx0.5001X。0.2510102x0.1251011033x40.06251011104x50.0312510111

7、105x60.015625101111106x70.00781251011111107xn0.0078125111111117(3)香农编码效率:/、Iclcl/lrlrK=/kp(x)=xl+x2+x3+x4+x5+x6+x7+x7i/248l63264l28l28i=l.984竺=竺=豎=loo%RKl.984费诺编码效率:/、lilclclrl,lrlriii=l.984K=kp(x)=xl+x2+x3+x4+x5+x6+x7+x7248l63264l28l28HX2=HX1=竺=loo%RKl.984(4)xp(x)编码码字kx0.5001X。0.25111x0.125202023x40.06251212x50.03125202203x60.01562512213x70.0078