信息論與編碼答案

1、5.1設(shè)信源Xa1a2as0.18a40.170.15a0.1a70.01p(X)0.2 0.19(1)求信源熵H(X)；(2)編二進(jìn)制香農(nóng)碼；(3)計算平均碼長和編碼效率解：(1)H(X)7p(a)log2 p(ai)i 10.2log2 0.2 0.19 log 0.190.18log20.18 0.17 log2 0.17 0.15lOg20.15 0.1log 2 0.10.01log2 0.012.609bit/symbolaiP(ai)Pa(aj)ki碼字a10.203000a20.190.23001a30.180.393011a40.170.573100a50.150.74310

2、1a60.10.8941110a70.010.9971111110_7K keg 0.2 3 0.19 3 0.18 3 0.17 3 0.15 3i 10.1 4 0.01 73.1415.2H(X)RH(X)/K 2.609 3.14183.1%對習(xí)題5.1的信源編二進(jìn)制費(fèi)諾碼，計算編碼效率解:aiP(ai)編碼碼字kia10.200002a20.19100103a30.1810113a40.1710102a50.15101103a60.11011104a70.01111114= i74Jt X 2745.3對信源X 二耳 £ 嶼 百屯七工r ； flCAoJ-pjl 019 O

3、JS 0L17 0J5 01 001/編二進(jìn)制和三進(jìn)制哈夫曼碼，計算各自的平均碼長和編碼效率解：二進(jìn)制哈夫曼碼：XiP(Xi)編碼碼字kiS61S50.610S40.391S30.350S20.261X10.20102X20.191112X30.1800003X40.1710013X50.1500103Si0.111X60.1001104X70.01101114= 2.72三進(jìn)制哈夫曼碼:Xip(Xi)編碼碼字kiS31S20.540S10.261X10.2221X20.190002X30.181012X40.172022X50.150X60.11X70.012112122102= 1x0+2

4、x(019+018+0117+015+01+005i=1戈jrcn*尿2 m2609i_axioga5= 914%5.4X設(shè)信源% £冷斗屯丸 r,12 4 8 16 32 64 12S 128求信源熵H(X);(2) 編二進(jìn)制香農(nóng)碼和二進(jìn)制費(fèi)諾碼；(3) 計算二進(jìn)制香農(nóng)碼和二進(jìn)制費(fèi)諾碼的平均碼長和編碼效率；(4) 編三進(jìn)制費(fèi)諾碼；(5) 計算三進(jìn)制費(fèi)諾碼的平均碼長和編碼效率；解：(1)刃(旳二-遲戸(斗)噸2 P©=卜蚯工"卜氐"卜T8+gxlng+吉淇Ing亠£ xlog工64+島漢電128十島24&lo326412X128= 1_

5、M4 Mfsymhoi二進(jìn)制香農(nóng)碼:XiP(Xi)Pa(Xi)ki碼字X10.5010X20.250.5210X30.1250.753110X40.06250.87541110X50.031250.9375511110X60.0156250.968756111110X70.00781250.98437571111110X80.00781250.992187571111111二進(jìn)制費(fèi)諾碼:XiP(Xi)編碼碼字kiX10.5001X20.2510102X30.125101103X40.0625011104X50.03125011110511X60.015625101111106X70.00781

6、251011111107X80.0078125111111117香農(nóng)編碼效率:=x<5+x7+ x7i 12&16326412812S= 1_M4/TW=ffi) = 14=100%Jt K 1984費(fèi)諾編碼效率：U8X?f 12SX7Xip(Xi)編碼碼字kiX10.5001X20.25111X30.12520202X40.06251212X50.03125202203X60.01562512213X70.00781252022204X80.0078125122214=丄刈十丄十丄"2十2刈脅丄為廿卄丄_并4V24&163264128123=132&R

7、1328 旬ogQ先把信源序列編成數(shù)字0, 1, 2,8,再替換成二進(jìn)制變長碼字，如下表所示5.5ru° 1設(shè)無記憶二進(jìn)制信源L氏201(1) 驗(yàn)證碼字的可分離性；(2) 求對應(yīng)于一個數(shù)字的信源序列的平均長度心;(3) 求對應(yīng)于一個碼字的信源序列的平均長度心；(4) 計算疋I ,并計算編碼效率；(5) 若用4位信源符號合起來編成二進(jìn)制哈夫曼碼，求它的平均碼長蠱，并計算編碼效率.序列數(shù)字二元碼字101000011100100131010000131011000014110000000151101000000161110000000017111100000000805.6 有二元平穩(wěn)馬氏

8、鏈，已知 p(0/0) = 0.8，p(1/1) = 0.7，求它的符號熵.用三個符號合成一個來編寫二進(jìn)制哈夫曼碼，求新符號的平均碼字長度和編碼效率5.7 對題5.6的信源進(jìn)行游程編碼若“ 0”游程長度的截至值為16,“1 ”游程長度的截至值為8，求編碼效率.5.8 選擇幀長N = 64(1) 對 0010000000000000000000000000000001000000000000000000000000000000 遍 L-D 碼；(2) 對 1000010000101100000000010010000101001000000001110000010000000010 遍L-D碼再譯碼；(3) 對 0000000000000000000000000000000000000