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# 2 20 201 s huffman huffman 3 sa sa a 1 a 2 a 3

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Unformatted text preview: 信源序列分组定理 信源序列分组定理 总可以找到N 0 离散无记忆信源 长度为N N 0的信源序列 任意给定 0， 0 序列 x 使得 都可以分成两组 ① 出现的概率 p( x) 满足： 1 log p( x) H ( X ) N (5.2.3) ② 所有符号序 列出现概率 之和小于 证： 设信源符号集 为 A {a1 , a2 , aq } ， 各符号出现的概率分别为 pi ， x x1 x2 xN 为长度为 N 的序列，N 为 x 中符号 ai i 出现的次数。 将信源序列按下列原则分成两 ：G1、 G2 ，其中， Ni G1 ： { x : pi , i 1,, q} N G2 ： { x : 其它} 根据大数定律，当序列足够长时，信源符号 a i G 出现的次数接近 Np i 。因此， 1 中的序列的符号出 现的次数符合大数定律，称典型序列。 可以看出 G 可以看出， 1 随 的不同而改变。 设 x G1 ，则对于 x 中的信源符号 a i ，有 Ni pi , i 1,...
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