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第六百八十六章 汉明码(纠错码)(1 / 2)

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信号在传输的过程中会不可避免的发生错误,而纠错码就可以发现和改正这个错误。

1948年,香农在《通信的数学理论》中信道编码定理指出:只要采用适当的纠错码,就可以在多类信道撒谎能够传输消息,误码率可以很小。

1950年,汉明发现了可以纠正一个独立错误的线性分组码。

格雷给粗一种可以纠正三个错误的完备码。

海明码(Hamming Code)是一个可以有多个校验位,具有检测并纠正一位错误代码的纠错码,所以它也仅用于信道特性比较好的环境中,如以太局域网中,因为如果信道特性不好的情况下,出现的错误通常不是一位。

海明码的检错、纠错基本思想是将有效信息按某种规律分成若干组,每组安排一个校验位进行奇偶性测试,然后产生多位检测信息,并从中得出具体的出错位置,最后通过对错误位取反(也是原来是1就变成0,原来是0就变成1)来将其纠正。

要采用海明码纠错,需要按以下步骤来进行:1、计算校验位数;2、确定校验码位置;3、确定校验码;4、实现校验和纠错

1.计算校验位数

要使用海明码纠错,首先就要确定发送的数据所需要要的校验码(也就是“海明码”)位数(也称“校验码长度”)。它是这样的规定的:假设用N表示添加了校验码位后整个信息的二进制位数,用K代表其中有效信息位数,r表示添加的校验码位,它们之间的关系应满足:N=K+r≤2r-1

如K=5,则要求2r?r≥5+1=6,根据计算可以得知r的最小值为4,也就是要校验5位信息码,则要插入4位校验码。如果信息码是8位,则要求2 r? r≥ 8 + 1 = 9,根据计算可以得知r的最小值也为4。

信息码位数与校验码位数之间的关系

信息码位数分别为1、2~4、5~11、12~26、27~57、58~120、121~247的时候,则校验码位数分别为2、3、4、5、6、7、8。

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