ABSTRACT
This chapter, the most hardware–friendly soft–decision Reed–Solomon decoding algorithms are the generalized minimum-distance (GMD) algorithm and the Chase algorithm. The GMD decoder assigns erasures to the least reliable code positions and tries multiple test vectors with erasures. The Chase decoder, the test vectors are formed by flipping the least reliable bits. The chapter introduces the Algebraic soft–decision (ASD) algorithms. The ASD algorithms are better explained by interpreting the codeword symbols as evaluation values of the message polynomial. The chapter discussees systematic encoding can be used when ASD decoding is adopted. The ASD algorithms try to recover the message polynomial through assigning larger multiplicities to more reliable points according to the channel information. This is actually the first step of ASD algorithms. Although different ASD algorithms have different multiplicity assignment schemes, they share the same interpolation and factorization steps.
