Howtosignalprocessing
- How does the Reed-Solomon method work?
- How does Reed-Solomon encoding work?
- Are Reed-Solomon codes MDS?
How does the Reed-Solomon method work?
A Reed-Solomon decoder attempts to identify the position and magnitude of up to t errors (or 2t erasures) and to correct the errors or erasures. This is a similar calculation to parity calculation. A Reed-Solomon codeword has 2t syndromes that depend only on errors (not on the transmitted code word).
How does Reed-Solomon encoding work?
Reed–Solomon codes are able to detect and correct multiple symbol errors. By adding t = n − k check symbols to the data, a Reed–Solomon code can detect (but not correct) any combination of up to t erroneous symbols, or locate and correct up to ⌊t/2⌋ erroneous symbols at unknown locations.
Are Reed-Solomon codes MDS?
Codes which achieve this bound, i.e for which n = k+d−1, are called MDS codes (Maximal Distance Separable). What we just showed is that Reed-Solomon codes are MDS codes.
