Claims Analysis
Total Claims: 3
Claim 1
Independent Claim
331 words
A process for realizing mappings between codewords of two distinct (N,K) Reed-Solomon codes over GF(2 J ) having selected two independent parameters: J, specifying the number of bits per symbol; and E, the symbol error correction capability of the code, wherein said independent parameters J and E yield the following: N=2 J -1, total number of symbols per codeword; 2E, the number of symbols assigned a role of check symbols; and K=N-2E, the number of code symbols representing information, all within a codeword of an (N,K) RS code over GF(2 J ), and having selected said parameters for encoding, the implementation of a decoder are governed by: 2 J field elements defined by a degree J primitive polynomial over GF(2) denoted by F(x); a code generator polynomial of degree 2E containing 2E consecutive roots of a primitive element defined by F(x); and, in a Berlekamp RS code, the basis in which the RS information and check symbols are represented, said process comprising the sequential steps of: first, symbol-by-symbol conversion due to root power translation of words R B .1 of a first RS code B to words R B .2, second, permutation of symbols of words R B .2 to yield words R B .3, third, symbol-by-symbol conversion of words R B .3 to words R G of a second RS code G, fourth, decoding words R G by correcting erroneous symbols in words R G using check symbols of each of said words R G for the information symbols in each word R G to obtain corrected words C G , and fifth, transformation of said corrected words C G back to said code B by the inverse of said third, second and first steps in that reverse sequence to convert codewords C G to codeword C B .3, to permute codewords C B .3 to yield codewords C B .2, and symbol-by-symbol conversion due to root power translation to convert codewords C B .2 to codewords C B .1.
Claim 2
Dependent Claim
331 words
A process for realizing mappings between codewords of two distinct (N,K) Reed-Solomon codes over GF(2 J ) having selected two independent parameters: J, specifying the number of bits per symbol; and E, the symbol error correction capability of the code, wherein said independent parameters J and E yield the following: N=2 J -1, total number of symbols per codeword; 2E, the number of symbols assigned a role of check symbols; and K=N-2E, the number of code symbols representing information, all within a codeword of an (N,K) RS code over GF(2 J ), and having selected said parameters for encoding, the implementation of a decoder are governed by: 2 J field elements defined by a degree J primitive polynomial over GF(2) denoted by F(x); a code generator polynomial of degree 2E containing 2E consecutive roots of a primitive element defined by F(x); and, in a Berlekamp RS code, the basis in which the RS information and check symbols are represented, said process comprising the sequential steps of: first, symbol-by-symbol conversion due to root power translation of words R B .1 of a first RS code B to words R B .2, second, permutation of symbols of words R B .2 to yield words R B .3, third, symbol-by-symbol conversion of words R B .3 to words R G of a second RS code G, fourth, decoding words R G by correcting erroneous symbols in words R G using check symbols of each of said words R G for the information symbols in each word R G to obtain corrected words C G , and fifth, transformation of said corrected words C G back to said code B by the inverse of said third, second and first steps in that reverse sequence to convert codewords C G to codeword C B .3, to permute codewords C B .3 to yield codewords C B .2, and symbol-by-symbol conversion due to root power translation to convert codewords C B .2 to codewords C B .1.
Claim 3
Dependent Claim
113 words
A process as defined in claim 1 wherein said words R B .1 of said first code B are defined by a function F(x) wherein said RS symbols are represented in another representation using a parameter λ for a field element where 1, λ, λ 2 , . . . , λ r-1 is a basis in GF(2 r ), and said process includes an initial step of converting symbol-to-symbol words C B of a first basis to said words R B of a second basis and a final step of said reverse sequence of steps for symbol-to-symbol conversion from said second basis to said first basis of representation using said parameter λ.