Reed-solomon encoder and decoder
AssigneeVitesse Semiconductor Corporation
InventorsSatish Sridharan, Michael Jarchi
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Abstract
A semi-parallel forward error correction system. In one embodiment the forward error correction system includes a semi-parallel Reed-Solomon encoder and a semi-parallel Reed-Solomon decoder. Information symbols comprised of bytes are provided eight bytes in parallel to an encoder which in parallel forms eight bytes of a nonsystematic code word. On decoding, a code word is provided to a time multiplexed syndrome generator and key equation solver. An error locator polynomial from the key equation solver and the syndromes from the syndrome generator are provided to an error location and error magnitude unit, which includes a plurality of polynomial evaluator units which process an error locator polynomial in parallel.
Claims5
A method of performing semi-parallel encoding and decoding of a data stream comprised of k-symbol information words using an (n,k) non-systematic code, the method comprising:
- sequentially providing a plurality of sets of a plurality of information symbols to an encoder, each set of the sets of the plurality of information symbols being less than k symbols, each set of the sets of the plurality of information symbols being subsets of information symbols of a k-symbol information word;
- sequentially performing Galois field multiplication on each set of the sets of a plurality of information symbols to form sets of codeword symbols of an n-symbol codeword;
- sequentially generating n-k syndromes;
- determining an error locator polynomial using the n-k syndromes;
- and
- evaluating a plurality of roots of the error locator polynomial using a plurality of polynomial evaluators, each polynomial evaluator evaluating a plurality of the roots of the error locator polynomial.
A method of performing semi-parallel encoding of a data stream comprised of k-symbol information words using an (n,k) non-systematic code, the method comprising:
- sequentially providing sets of a plurality of information symbols to an encoder, the sets of the plurality of information symbols together forming a k-symbol information word;
- and
- sequentially performing Galois field multiplication on each set of the plurality of information symbols to form sets of codeword symbols of an n-symbol codeword.
A method of performing semi-parallel decoding using an (n,k) code, the method comprising:
- providing a codeword to a syndrome generator;
- sequentially generating n-k syndromes by multiplying each symbol of the codeword by a Galois field element to form first syndrome intermediate terms and combining the first syndrome intermediate terms on a first clock cycle and multiplying each first syndrome intermediate term by a Galois field element to form second syndrome intermediate terms and combining the second syndrome intermediate terms on a second clock cycle;
- determining an error locator polynomial using the n-k syndromes;
- evaluating a plurality of roots of the error locator polynomial using a plurality of polynomial evaluators, each polynomial evaluator evaluating a plurality of the roots of the error locator polynomial.
Dependencies are inferred from the claim text.