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Bit-Serial Reed-Solomon Encoders

[bit_serial_rs_encoder graphic]

The figure depicts a portion of Berlekamp's Bit-Serial Reed-Solomon Encoder, which is NASA's standard for deep-space 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 2m over the field of order 2, a fact which almost contradicts the elementary theorem that the Galois field of order 2m is unique, and that all bases define the same field.

"Bit-Serial Reed-Solomon Encoders", IEEE Trans Inform Theory, IT28:869-874 (1982).