信息论与编码第五章答案

1、5.1设信源(1)求信源熵H(X)；(2)编二进制香农码；(3)计算平均码长和编码效率.解：(1)(2)aip(ai)pa(aj)ki码字a10.203000a20.190.23001a30.180.393011a40.170.573100a50.150.743101a60.10.8941110a70.010.9971111110(3)5.2对习题5.1的信源编二进制费诺码，计算编码效率.解：aip(ai)编码码字kia10.200002a20.19100103a30.1810113a40.1710102a50.15101103a60.11011104a70.011111145.3对信源编二进

2、制和三进制哈夫曼码，计算各自的平均码长和编码效率.解：二进制哈夫曼码：xip(xi)编码码字kis61s50.610s40.391s30.350s20.261x10.20102x20.191112x30.1800003x40.1710013x50.1500103s10.111x60.1001104x70.01101114三进制哈夫曼码：xip(xi)编码码字kis31s20.540s10.261x10.2221x20.190002x30.181012x40.172022x50.150102x60.11112x70.0121225.4设信源(1)求信源熵H(X)；(2)编二进制香农码和二进制费诺

3、码；(3)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；(4)编三进制费诺码；(5)计算三进制费诺码的平均码长和编码效率；解：(1)(2)二进制香农码：xip(xi)pa(xi)ki码字x10.5010x20.250.5210x30.1250.753110x40.06250.87541110x50.031250.9375511110x60.0156250.968756111110x70.00781250.98437571111110x80.00781250.992187571111111二进制费诺码：xip(xi)编码码字kix10.5001x20.2510102x30.12510110

4、3x40.06251011104x50.0312510111105x60.015625101111106x70.00781251011111107x80.0078125111111117(3)香农编码效率：费诺编码效率：(4)xip(xi)编码码字kix10.5001x20.25111x30.12520202x40.06251212x50.03125202203x60.01562512213x70.00781252022204x80.0078125122214(5)5.5设无记忆二进制信源先把信源序列编成数字0，1，2，8，再替换成二进制变长码字，如下表所示.(1)验证码字的可分离性；(2)求

5、对应于一个数字的信源序列的平均长度；(3)求对应于一个码字的信源序列的平均长度；(4)计算，并计算编码效率；(5)若用4位信源符号合起来编成二进制哈夫曼码，求它的平均码长，并计算编码效率.序列数字二元码字101000011100100131010000131011000014110000000151101000000161110000000017111100000000805.6有二元平稳马氏链，已知p(0/0) = 0.8，p(1/1) = 0.7，求它的符号熵.用三个符号合成一个来编写二进制哈夫曼码，求新符号的平均码字长度和编码效率.5.7对题5.6的信源进行游程编码.若“0”游程长度的截至值为16，“1”游程长度的截至值为8，求编码效率.5.8选择帧长N= 64(1)对0010000000000000000000000000000001000000000000000000000000000000遍L-D码；(2)对1000010000101100000000010010000101001000000001110000010000000010遍L-D码再译码；(3)对0000000000000000000000000000000000000000000000000000000000000000遍L-D码；(4)对10100011010111