Reed–Solomon Codes
Reed–Solomon Codes
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DOI：
10.1002/9780470035726.ch5
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发表时间：
2006-11
期刊：
影响因子：
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通讯作者：
J. C. Moreira;P. Farrell
中科院分区：
文献类型：
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作者：
J. C. Moreira;P. Farrell
Reed-Solomon (RS) 码是一种纠错码，最早由 Reed 和 Solomon 在 1960 年的论文中描述[9]。从那时起，它们就被应用于 CD-ROM、无线通信、空间通信、DSL、DVD 和数字电视。 RS 编码数据相对简单，但解码非常耗时，尽管 Berlekamp 等人在 1960 年代取得了重大效率改进 [2,5,6,8]。直到最近几年，使用 RS 发送高带宽数据才在计算上成为可能。 RS 与汉明码的不同之处在于，RS 对位组进行编码，而不是一次对一位进行编码。我们将这些组称为“数字”（也称为“符号”或“系数”）。当且仅当一个数字的所有位都没有错误时，该数字才是没有错误的。例如，如果一个数字是一个 8 位字符，并且同一单个字符的 3 位出错，我们将把它算作一个损坏的数字。以下示例中有两个损坏的数字（但损坏的位多于两个）。
A Reed-Solomon (RS) code is an error-correcting code first described in a paper by Reed and Solomon in 1960 [9]. Since that time they’ve been applied in CD-ROMs, wireless communications, space communications, DSL, DVD, and digital TV. RS encoding data is relatively straightforward, but decoding is timeconsuming, despite major efficiency improvements made by Berlekamp and other during the 1960’s [2, 5, 6, 8]. Only in the past few years has it become computationally possible to send high-bandwidth data using RS. RS differs from a Hamming code in that it encodes groups of bits instead of one bit at a time. We will call these groups “digits” (also “symbols” or “coefficients”). A digit is error-free if and only if all of its bits are error-free. For instance, if a digit is an 8-bit character, and three bits of the same single character are in error, we will count that as one corrupted digit. There are two corrupted digits (but more than two corrupted bits) in the following example.