 

BitSerial ReedSolomon Encoders The figure depicts a portion of Berlekamp's BitSerial ReedSolomon Encoder, which is NASA's standard for deepspace probes. Since the more complicated decoder is located on the ground, minimization of encoder power and weight is crucial. RS Encoders must perform many finite field multiplications, which in the 1970s were routinely implemented in a standard way. Berlekamp simplified the design enormously, yielding RS Encoders that are even simpler than encoders for cyclic binary codes of the same redundancy. One crucial step is the selection of a nonconventional basis for the representation of the field of order 2^{m} over the field of order 2, a fact which almost contradicts the elementary theorem that the Galois field of order 2^{m} is unique, and that all bases define the same field. "BitSerial ReedSolomon Encoders", IEEE Trans Inform Theory, IT28:869874 (1982).  