CRC计算和BCH编码[理论] [英] CRC calculating and BCH encoding [THEORY]

问题描述

我对BCH编码有疑问. BCH编码是否与CRC余数计算一样的操作? M(x)mod G(x)= R(x)和R(x)是我的BCH代码吗?

I have question about BCH Encoding. Is BCH Encoding is the same operation like CRC remainder calculation? M(x) mod G(x) = R(x) and R(x) is my BCH code?

推荐答案

您非常正确.确切地说，如果生成多项式为 g(x)，而块大小为 n ，则有效代码字为 g(x)的倍数，其度< n .

You are pretty much correct. To be precise, if your generator polynomial is g(x) and your block size is n, then the valid code words are the multiples of g(x) with degree < n.

假设您收到的消息 m(x)为度< k 和 g(x)具有 n-k 度:您可以通过多种方式将邮件转换为唯一的有效代码字.例如， m(x)* g(x)可以很好地工作……但是我们通常希望代码字以我们的实际消息开头，然后是一些校验位.在这种情况下，代码字是:

Lets say you have a message m(x) of degree < k, and g(x) has degree n-k: There are different ways you could turn your message into a unique valid code word. m(x)*g(x) works fine, for example... But we commonly want the code word to start with our actual message, followed by some check bits. In that case, the code word is:

m(x)* x ^(n-k)-(m(x)* x ^(n-k)mod g(x))

大多数 CRC校验也以这种方式计算，因为CRC代码和BCH代码都是多项式代码( https://en.wikipedia.org/wiki/Polynomial_code ).它们只是具有不同的生成多项式.

Most CRC checks are calculated in exactly this way as well, since CRC codes and BCH codes are both polynomial codes (https://en.wikipedia.org/wiki/Polynomial_code). They just have different generator polynomials.

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