Methods and apparatus for coding and decoding data using Reed-Solomon codes
First Claim
1. A method for encoding data, comprising:
- (a) providing a first table of first component values multiplied by code generator coefficients and a second table of second component values multiplied by the code generator coefficients;
(b) determining a Galois field element based on a message symbol and a high order remainder symbol;
(c) separating the Galois field element into first and second components;
(d) using the first component and a generator coefficient index to access one or more first table values in the first table and using the second component and the generator coefficient index to access one or more second table values in the second table,(e) determining a current remainder symbol based on first and second table values having equal generator coefficient indices, and a previous remainder symbol;
(f) performing step (e) for each generator coefficient of the code generator to provide a group of remainder symbols; and
(g) performing steps (b)–
(f) for each message symbol in a codeword to provide a group of final remainder symbols which constitute check symbols to be transmitted with the message symbols of the codeword.
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Abstract
Methods and apparatus are provided for encoding data. The method includes (a) providing a first table of first component values multiplied by code generator coefficients and a second table of second component values multiplied by the code generator coefficients, (b) determining a Galois field element based on a message symbol and a high order remainder symbol, (c) separating the Galois field element into first and second components, (d) using the first component and a generator coefficient index to access one or more first table values in the first table and using the second component and the generator coefficient index to access one or more second table values in the second table, (e) determining a current remainder symbol based on first and second table values having equal generator coefficient indices, and a previous remainder symbol, (f) performing step (e) for each generator coefficient of the code generator to provide a set of remainder symbols, and (g) performing steps (b)–(f) for each message symbol in a codeword to provide a set of final remainder symbols which constitute check symbols to be transmitted with the message symbols of the codeword.
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Citations
24 Claims
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1. A method for encoding data, comprising:
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(a) providing a first table of first component values multiplied by code generator coefficients and a second table of second component values multiplied by the code generator coefficients; (b) determining a Galois field element based on a message symbol and a high order remainder symbol; (c) separating the Galois field element into first and second components; (d) using the first component and a generator coefficient index to access one or more first table values in the first table and using the second component and the generator coefficient index to access one or more second table values in the second table, (e) determining a current remainder symbol based on first and second table values having equal generator coefficient indices, and a previous remainder symbol; (f) performing step (e) for each generator coefficient of the code generator to provide a group of remainder symbols; and (g) performing steps (b)–
(f) for each message symbol in a codeword to provide a group of final remainder symbols which constitute check symbols to be transmitted with the message symbols of the codeword. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
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13. Apparatus for encoding data, comprising:
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a first lookup table containing first component values multiplied by code generator coefficients; a second lookup table containing second component values multiplied by the code generator coefficients; and a processor comprising means for determining a Galois field element based on a message symbol and a high order remainder symbol, means for separating the Galois field element into first and second components, means, using the first component and a generator coefficient index, for accessing one or more first table values in the first lookup table, means, using the second component and the generator coefficient index, for accessing one or more second table values in the second table; and
means for determining a current remainder symbol, based on first and second table values having equal generator coefficient indices, and a previous remainder symbol, for each generator coefficient of the code generator to provide a group of remainder symbols, wherein each message symbol of a codeword is processed to provide a group of final remainder symbols which constitute check symbols to be transmitted with the message symbols of the codeword. - View Dependent Claims (14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24)
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Specification