Introduction to RS Codec
Concept of Forward Error Correction
- Add redundancy to a message in order to eliminate the need of retransmission by error correction.
Theory
- Reed Solomon coding operates on a finite field called Galios Field.
- Generator polynomial: G(x) = (x-a0)(x-a1) · · ·(x-a2t-1), where a is a root of the binary primitive polynomial x8+x4+x3+x2+1.
- Message polynomial: M(x)=(Mk-1xk-1+ Mk-2xk-2 + … + M1x1 + M0 )•x2t-1
- Check polynomial: C(x)=M(x) / G(x)
= C2t-1x2t-1+ C2t-2x2t-2 + … + C1x1 + C0
- Encoded codes: (Mk-1 , Mk-2 , …, M0 , C2t-1 , C2t-2 , …, C0 )