Bit-Serial RS Encoders

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 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.

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

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Home Publications Videos Research Interests Algorithms Polynomial Factorization Algebraic Decoding Bit-Serial Encoding Applied Analysis Games Complexity Computer Architecture Finance Business Information Theory Philanthropy Thesis Students Awards Board Memberships K-12 Outreach Education / Employment Biographies Contact Information and Site Credits Site Map	Bit-Serial Reed-Solomon Encoders 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 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. "Bit-Serial Reed-Solomon Encoders", IEEE Trans Inform Theory, IT28:869-874 (1982).