Parallel finite field vector operators
First Claim
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1. A finite field vector calculation circuit, comprising:
- an interface configured to receive a codeword associated with a data stream and split the codeword into a plurality of symbols;
a plurality of multiplication circuits configured to receive the plurality of symbols and generate a plurality of expanded polynomials;
an exclusive OR (XOR) circuit configured to combine the plurality of expanded polynomials to generate an XOR output and forward said XOR output to a reduction circuit, wherein the reduction circuit performs a modulo reduction of the XOR output to generate a plurality of separate products.
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Abstract
Parallel Reed Solomon error correction can be performed using dot products in finite fields while factoring out multiplier reduction. A finite field accumulator with left and right shifts of the polynomial dot products is used to generate the final result using a fixed dot product core and a small number of post processing Galois Field multiplies. An efficient Reed Solomon decoder for transmission, storage, and processing operations can be implemented in a small area while being easily scalable.
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18 Claims
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1. A finite field vector calculation circuit, comprising:
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an interface configured to receive a codeword associated with a data stream and split the codeword into a plurality of symbols; a plurality of multiplication circuits configured to receive the plurality of symbols and generate a plurality of expanded polynomials; an exclusive OR (XOR) circuit configured to combine the plurality of expanded polynomials to generate an XOR output and forward said XOR output to a reduction circuit, wherein the reduction circuit performs a modulo reduction of the XOR output to generate a plurality of separate products. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13)
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14. A syndrome calculation circuit, comprising:
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multiplication circuitry configured to combine a plurality of operands associated with a data stream to generate a plurality of expanded polynomials; an exclusive OR (XOR) circuit configured to combine the plurality of expanded polynomials multiplier results to generate an XOR output and forward said XOR output to a reduction circuit, wherein the reduction circuit performs a modulo reduction of the XOR output to generate a plurality of separate products used for syndrome calculation. - View Dependent Claims (15, 16, 17, 18)
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Specification