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第一章:异前置码(即时码) ^1SZ8ymrW
比如信源符号是「a(概率 0.6)、b(0.3)、c(0.1)」
1、a→0(短码,因为常出现)
2、b→10(中码)
3、c→111(长码,不常出现) ^dmcnHTGB
克拉夫特不等式是 “能构成异前置码的必要条件,不是充分条件”—— 满足不等式可能构成,但不满足一定不能构成。 ^hhdElqHC
考试中只要记住 “异前置码的码长对应二叉树层级,占用节点数之和不超过最大层总节点数” 即可 ^oG6PA9Uo
应用题: ^yOh7uu9C
平均码长L是每个符号对应的 “码字长度” 按概率加权后的平均值—— 简单说,就是 “发一个符号,平均要用多少个码元(0/1)”。 ^ZFZ02c4c
编码效率是衡量 “编码有多‘紧凑’” 的指标,核心是看编码的平均码长和 “理论最短码长(信源熵)” 的接近程度 ^ddunARwM
详见PPT内容。 ^8VloY5zL
一、费诺码 “按概率从大到小” 是固定构造规则 ^uxlEKsku
费诺码的核心逻辑就是 “给概率大的符号 / 扩展消息编短码”,所以必须先按概率降序排列,这是构造费诺码的默认步骤(考试中必须这么做)。 ^8JO39Uxc
消息序列 “0102001001” 的概率表可以导出 ^dKeHfGZz
所以按照概率编码,0->0, 1->10, 2->11。 ^8ih7snyI
此消息序列如果按照2次扩展来编码,方法如下: ^v4URLm0R
[0.36, 0.18, 0.06, 0.18, 0.09, 0.03, 0.06, 0.03, 0.01]对应
[00, 01, 02, 10, 11, 12, 20, 21, 22] ^uwdgTkos
从大到小排列
[0.36,0.18,0.18,0.09,0.06,0.06,0.03,0.03,0.01]对应
[00, 01, 10, 11, 02, 20, 12, 21, 22] ^x6FyVyq7
分别编码
00, 01, 100, 101, 1100, 1101, 1111, 11100, 11101 ^IVwxCzXN
所以编码之后,就变成00->00, 02->1100, 10->100, 01->01 ^CX5kpqva
习题总结:
- 已知马尔科夫信源,条件概率矩阵,求熵率和极限熵。
- 已知信息源概率,求对二次扩展信源编出二进制费诺码的码表,
编码效率η。 ^1hoCoN3B
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