ABSTRACT
This chapter introduces the construction of Reed–Solomon (RS) codes. It explains traditional hard–decision decoding algorithms, such as the Peterson–Gorenstein–Zierler algorithm and Berlekamp–Massey algorithm (BMA), and their implementation architectures. The decoders are currently employed in practical applications due to the existence of efficient and high–speed hardware implementations. The hard–decision decoder, each received symbol takes one of the possible values. These decoders have lower complexity but cannot correct as many errors as soft–decision decoders, in which the probability information from the channel is used to decide the likely values for each received symbol. The hard–decision RS decoders discussed so far is error–only decoders. They find both the locations and magnitudes of the errors. Instead of making hard decisions, the unreliable symbols can be set as erasures. Erasure–and-error decoding is the simplest type of soft-decision decoding. It can be implemented by modifying the inputs to the BMA.
