信源編碼習(xí)題答案

1、.5.1 設(shè)信源(1) 求信源熵H(X)；(2) 編二進制香農(nóng)碼；(3) 計算平均碼長和編碼效率。解：(1)(2)xip(xi)pa(xi)ki碼字x10.203000x20.190.23001x30.180.393011x40.170.573100x50.150.743101x60.10.8941110x70.010.9971111110(3)5.2 對信源編二進制費諾碼，計算編碼效率。解：xip(xi)編碼碼字kix10.200002x20.19100103x30.1810113x40.1710102x50.15101103x60.11011104x70.011111145.3 對信源編二

2、進制和三進制哈夫曼碼，計算各自的平均碼長和編碼效率。解：二進制哈夫曼碼：xip(xi)編碼碼字kis61s50.610s40.391s30.350s20.261x10.20102x20.191112x30.1800003x40.1710013x50.1500103s10.111x60.1001104x70.01101114三進制哈夫曼碼：xip(xi)編碼碼字kis31s20.540s10.261x10.2221x20.190002x30.181012x40.172022x50.150102x60.11112x70.0121225.4 設(shè)信源(1) 求信源熵H(X)；(2) 編二進制香農(nóng)碼和二

3、進制費諾碼；(3) 計算二進制香農(nóng)碼和二進制費諾碼的平均碼長和編碼效率；(4) 編三進制費諾碼；(5) 計算三進制費諾碼的平均碼長和編碼效率；解：(1)(2)二進制香農(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制費諾碼：xip(xi)編碼碼字kix10.5001x20.2510102x30.1

4、25101103x40.06251011104x50.0312510111105x60.015625101111106x70.00781251011111107x80.0078125111111117(3)香農(nóng)編碼效率：費諾編碼效率：(4)xip(xi)編碼碼字kix10.5001x20.25111x30.12520202x40.06251212x50.03125202203x60.01562512213x70.00781252022204x80.0078125122214(5)5.5 設(shè)無記憶二進制信源先把信源序列編成數(shù)字0，1，2，8，再替換成二進制變長碼字，如下表所示。(1) 驗證碼字的

5、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；(3) 求對應(yīng)于一個碼字的信源序列的平均長度；(4) 計算，并計算編碼效率；(5) 若用4位信源符號合起來編成二進制哈夫曼碼，求它的平均碼長，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0000000000000000000000000000000000000000000000000000000000000000遍L-D碼