Decoding Reed–Solomon Codes

Years and Authors of Summarized Original Work

• 1999; Guruswami, Sudan

Problem Definition

In order to ensure the integrity of data in the presence of errors, an error-correcting code is used to encode data into a redundant form (called a codeword). It is natural to view both the original data (or message) as well as the associated codeword as strings over a finite alphabet. Therefore, an error-correcting code C is defined by an injective encoding map ${ E\!\!:\!\Sigma^k\!\rightarrow\!\!\Sigma^n }$, where k is called the message length, and n the block length. The codeword, being a redundant form of the message, will be longer than the message. The rate of an error-correcting code is defined as the ratio k/n of the length of the message to the length of the codeword. The rate is a quantity in the interval ${ (0,1] }$, and is a measure of the redundancy introduced by the code. Let R(C) denote the rate of a code C.

The redundancy built into a codeword enables detection and hopefully...