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1、5.1?設(shè)信源(1)?求信源熵H(X)；(2)?編二進(jìn)制香農(nóng)碼；(3)?計(jì)算平均碼長(zhǎng)和編碼效率。解：(1)(2)aip(ai)pa(aj)ki碼字a10.203000a20.190.23001a30.180.393011a40.170.573100a50.150.743101a60.10.8941110a70.010.9971111110(3)5.2?對(duì)習(xí)題5.1的信源編二進(jìn)制費(fèi)諾碼，計(jì)算編碼效率。解：aip(ai)編碼碼字kia10.200 002a20.1910 0103a30.181 0113a40.1710
2、102a50.1510 1103a60.11011104a70.01111114?5.3?對(duì)信源編二進(jìn)制和三進(jìn)制哈夫曼碼，計(jì)算各自的平均碼長(zhǎng)和編碼效率。解：二進(jìn)制哈夫曼碼：xip(xi)編碼碼字kis6 ?????1 s5 ????0.610 s4 ???0.39 1 s3 ??0.35 0 s2 ?0.26 1 x10.2 0? 102x20.19 1? 112x30.18 0?? 0003x40.17 1?? 0013x50.15 0??? 0103s1 0.111??? x60.1
3、0???? 01104x70.011 01114?三進(jìn)制哈夫曼碼：xip(xi)編碼碼字kis3???1 s2??0.540 s1?0.26?1 x10.2??221x20.19?0?002x30.18?1?012x40.17?2?022x50.150??102x60.11??112x70.012??1225.4?設(shè)信源(1)?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(jì)算二進(jìn)制香農(nóng)碼和二進(jìn)制費(fèi)諾碼的平均碼長(zhǎng)和編碼效率；(4)?編三進(jìn)制費(fèi)諾碼；(5)?計(jì)算三進(jìn)制費(fèi)諾碼的平均碼長(zhǎng)和編碼效
4、率；解：(1)(2)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kix10.50??????01x20.2510?????102x30.12510????1103x40.0625
5、10???11104x50.0312510??111105x60.01562510?1111106x70.00781251011111107x80.0078125111111117(3)香農(nóng)編碼效率：費(fèi)諾編碼效率：(4)xip(xi)編碼碼字kix10.50?? 01x20.251 ? 11x30.12520? 202x40.06251 212x50.0312520 2203x60.0156251 2213x70.00781252022204x80.0078125122214(5)?5.5?設(shè)無(wú)記憶二進(jìn)制信源先把信源序
6、列編成數(shù)字0，1，2，……，8，再替換成二進(jìn)制變長(zhǎng)碼字，如下表所示。(1)?驗(yàn)證碼字的可分離性；(2)?求對(duì)應(yīng)于一個(gè)數(shù)字的信源序列的平均長(zhǎng)度；(3)?求對(duì)應(yīng)于一個(gè)碼字的信源序列的平均長(zhǎng)度；(4)?計(jì)算，并計(jì)算編碼效率；(5)?若用4位信源符號(hào)合起來(lái)編成二進(jìn)制哈夫曼碼，求它的平均碼長(zhǎng)，并計(jì)算編碼效率。序列數(shù)字二元碼字101000011100100131010000131011000014110000000151101000000161110000000017111100000000805.6?有二元平穩(wěn)馬氏鏈，已知p(0/
7、0)=0.8，p(1/1)=0.7，求它的符號(hào)熵。用三個(gè)符號(hào)合成一個(gè)來(lái)編寫(xiě)二進(jìn)制哈夫曼碼，求新符號(hào)的平均碼字長(zhǎng)度和編碼效率。5.7?對(duì)題5.6的信源進(jìn)行游程編碼。若“0”游程長(zhǎng)度的截至值為16，“1”游程長(zhǎng)度的截至值為8，求編碼效率。5.8?選擇幀長(zhǎng)N?=64(1)?對(duì)0010000000000000000000000000000001000000000000000000000000000000遍L(zhǎng)-D碼；(2)?對(duì)10000100001011000000000100100001010010000000011100000
8、10000000010遍L(zhǎng)-D碼再譯碼；(3)?對(duì)0000000000000000000000000000000000000000000000000000000000000000遍L(zhǎng)-D碼；(4)?對(duì)10100011010111000110001110100110000111101100101000110101011
