Format of Reed-Solomon Codes
Reed Solomon codes are non binary cyclic codes with symbols made up of m-sequences.where m can be any natural number greater than 2.
For a given m, the length of all the Reed-Solomon codes composed of m-bit symbols is 2m - 1. For example, for 8-bit symbols, the length of the Reed-Solomon codes is 28 - 1 = 255.
A complete Reed-Solomon code consists of two parts: the data part and the parity part. For a Reed-Solomon code of n symbols, the first k symbols is the data part, which is the information to be protected against corruption, and the following (n-k) symbols is the parity part, which is calculated based on the data part. Such a Reed-Solomon code is referred to as an (n, k) Reed-Solomon code, or RS(n,k) code. The number of parity symbols is (n-k), usually an even number represented as 2t. A Reed-Solomon code with 2t parity symbols has the capability of correcting up to t error symbols.
Reed Solomon coding which I have implemented using simulink, has (n,k)=(7,4)with 8-PSK and (15,13) with 16-PSK.
where 't' is error correcting capability of code, and 'm' is number of bits per symbol.
Reed-Solomon codes is a linear systematic block code based on finite field theory. The systematic format, the efficient encoding and decoding algorithm, and the powerful error correction capability of the code make it one of the most widely used error correction codes in the industry.