What is Reed–Solomon Code?

When we transfer some data over a network then there are possibilities that data get corrupted due to some network problem. Bits inside data might get corrupted due to interference or some network problem. So there is the risk of data being lost during transfer.

Reed-Solomon codes

Reed-Solomon codes are the code that was introduced by Irving S. Reed and Gustave Solomon. Reed-Solomon code is a subclass of non-binary BCH codes. The encoder of Reed-Solomon codes differs from a binary encoder in that it operates on multiple bits rather than individual bits.

So basically, Reed-Solomon codes help in recovering corrupted messages that are being transferred over a network. In Reed-Solomon codes, we have:

Reed-Solomon codes encoder receives data and before transferring it over the noisy network it adds some parity bits with our original data bits.

On the other hand, we have a Reed-Solomon codes decoder that detects corrupted messages and recovers them from error.

Representation of n-bits Reed-Solomon codes

n-bits representation of the Reed-Solomon codes

n-bits representation of the Reed-Solomon codes

Parameters of Reed-Solomon code:

Generator function

In Reed-Solomon codes, the generator function is generated using a special polynomial. In Reed-Solomon codes, all valid codewords are exactly divisible by the generator polynomial. The generator function is given by:

g(x) = (x-α)(x-α 2 )(x-α 3 )……(x-α 2t )

Encoding

We perform encoding in Reed-Solomon codes with the following methods:

Decoding

At the receiver end we perform the following methods:

Application of Reed-Solomon codes

Advantages:

Here we will discuss how it is better than binary BCH codes.

Disadvantages:

Despite all these advantages of Reed-Solomon codes it also has some disadvantages in comparison with the BCH code.