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1. 发明授权

US06438724B1 Method and apparatus for deterministically altering cyclic redundancy check information for data storage 失效
标题翻译：用于确定性地改变用于数据存储的循环冗余校验信息的方法和装置
公开(公告)号：US06438724B1
公开(公告)日：2002-08-20
申请号：US09270069
申请日：1999-03-16
申请人： Charles Edwin Cox , James Lee Hafner , Martin Aureliano Hassner , Ralph Koetter , Arvind Motibhai Patel
发明人： Charles Edwin Cox , James Lee Hafner , Martin Aureliano Hassner , Ralph Koetter , Arvind Motibhai Patel
IPC分类号： H03M1315
CPC分类号： H03M13/093 , H03M13/1515 , H03M13/29 , H03M13/2903 , H03M13/2927
摘要： A method and apparatus for ensuring the integrity of data that can detect errors that remain when the data correction scheme fails to correct at least some of the errors, or has added additional errors. Reed-Solomon check symbols are used for error correction and cyclic redundancy check symbols are used to detect the remaining errors. The roots of the generator polynomials used to generate the Reed-Solomon check symbols and the cyclic redundancy check symbols meet a selected subset of a plurality of conditions. The roots are further selected so that the necessary exponentiation may be performed by a combination of exponentiations by powers of two and multiplications. The Reed-Solomon check symbols are generated based on the data portion of the data block. A deterministically altered data stream is generated based on the data portion of the data block and the cyclic redundancy check symbols are generated based on the deterministically altered data stream. The deterministically altered data stream is generated by performing an operation on a symbol of the data portion based on a position of the symbol within a Reed-Solomon codeword.
摘要翻译：一种用于确保数据完整性的方法和装置，其可以检测当数据校正方案无法校正至少一些错误时残留的数据，或者增加了额外的错误。 Reed-Solomon检查符号用于纠错，循环冗余校验符号用于检测剩余错误。用于产生Reed-Solomon检查符号和循环冗余校验符号的生成多项式的根符合多个条件的选定子集。进一步选择根，使得可以通过乘以幂的乘积的乘积的组合来执行必要的取幂。基于数据块的数据部分生成Reed-Solomon检查符号。基于数据块的数据部分生成确定性改变的数据流，并且基于确定性改变的数据流生成循环冗余校验符号。基于Reed-Solomon码字中的符号的位置，对数据部分的符号执行操作来生成确定性改变的数据流。

2. 发明授权

US06446234B1 Method and apparatus for updating cyclic redundancy check information for data storage 失效
标题翻译：用于更新用于数据存储的循环冗余校验信息的方法和装置
公开(公告)号：US06446234B1
公开(公告)日：2002-09-03
申请号：US09269000
申请日：1999-03-16
申请人： Charles Edwin Cox , James Lee Hafner , Martin Aureliano Hassner , Ralph Koetter , Arvind Motibhai Patel
发明人： Charles Edwin Cox , James Lee Hafner , Martin Aureliano Hassner , Ralph Koetter , Arvind Motibhai Patel
IPC分类号： H03M1315
CPC分类号： H03M13/093 , H03M13/1515 , H03M13/29 , H03M13/2903 , H03M13/2927
摘要： A method and apparatus for ensuring the integrity of data that can detect errors that remain when the data correction scheme fails to correct at least some of the errors, or has added additional errors. Reed-Solomon check symbols are used for error correction and cyclic redundancy check symbols are used to detect the remaining errors. The roots of the generator polynomials used to generate the Reed-Solomon check symbols and the cyclic redundancy check symbols meet a selected subset of a plurality of conditions. The roots are further selected so that the necessary exponentiation may be performed by a combination of exponentiations by powers of two and multiplications. The Reed-Solomon check symbols are generated based on the data portion of the data block. A deterministically altered data stream is generated based on the data portion of the data block and the cyclic redundancy check symbols are generated based on the deterministically altered data stream. The deterministically altered data stream is generated by performing an operation on a symbol of the data portion based on a position of the symbol within a Reed-Solomon codeword.
摘要翻译：一种用于确保数据完整性的方法和装置，其可以检测当数据校正方案未能校正至少一些错误时残留的错误，或者增加了额外的错误。 Reed-Solomon检查符号用于纠错，循环冗余校验符号用于检测剩余错误。用于产生Reed-Solomon检查符号和循环冗余校验符号的生成多项式的根符合多个条件的选定子集。进一步选择根，使得可以通过乘以幂的乘积的乘积的组合来执行必要的取幂。基于数据块的数据部分生成Reed-Solomon检查符号。基于数据块的数据部分生成确定性改变的数据流，并且基于确定性改变的数据流生成循环冗余校验符号。基于Reed-Solomon码字中的符号的位置，对数据部分的符号执行操作来生成确定性改变的数据流。

3. 发明授权

US06345376B1 Method and means for computationally efficient on-the-fly error correction in linear cyclic codes using ultra-fast error location 失效
标题翻译：用于使用超快速误差位置的线性循环码中计算高效的即时纠错的方法和装置
公开(公告)号：US06345376B1
公开(公告)日：2002-02-05
申请号：US09618414
申请日：2000-07-18
申请人： Charles Edwin Cox , Myron Dale Flickner , James Lee Hafner , Martin Aureliano Hassner , Barry Marshall Trager , Shmuel Winograd
发明人： Charles Edwin Cox , Myron Dale Flickner , James Lee Hafner , Martin Aureliano Hassner , Barry Marshall Trager , Shmuel Winograd
IPC分类号： H03M1300
CPC分类号： H03M13/1545 , H03M13/1515 , H03M13/616
摘要： A computationally efficient, machine-implementable method and means for detecting and correcting errors in received codewords on-the-fly within the capacity of a linear cyclic code using ultra-fast error location processing. Each error locator polynomial of degree t over a finite Galois field derived from a codeword syndrome is mapped into a matrix representative of a system of linear simultaneous equations related to the polynomial coefficients. Roots indicative of error locations within the codeword are extracted from the matrix by a modified Gaussian Elimination process for all the roots where t≦5 and at least one root plus a subset of candidate roots from the finite field for iterative substitution where t>5. Corrected values are separately determined and correction is secured by logically combining the corrected values with the codeword values in error at the error locations represented by the roots.
摘要翻译：一种计算有效的机器可实现的方法和装置，用于使用超快速错误位置处理在线性循环码的容量内即时检测和纠正接收到的码字中的错误。将来自码字综合征的有限伽罗瓦域的度t的每个误差定位多项式映射成表示与多项式系数相关的线性联立方程组的矩阵。通过对于t = 5的所有根的修正的高斯消除处理从矩阵中提取指示码字内的错误位置的根，并且对于迭代取代的t≥5，至少有一个根加上来自有限域的候选根的子集，其中t> 5 。单独确定校正后的值，并且通过将修正的值与由根表示的错误位置处的错误的码字值进行逻辑组合来确保校正。

4. 发明授权

US6154868A Method and means for computationally efficient on-the-fly error correction in linear cyclic codes using ultra-fast error location 失效
标题翻译：用于使用超快速误差位置的线性循环码中计算高效的即时纠错的方法和装置
公开(公告)号：US6154868A
公开(公告)日：2000-11-28
申请号：US896348
申请日：1997-07-18
申请人： Charles Edwin Cox , Myron Dale Flickner , James Lee Hafner , Martin Aureliano Hassner , Barry Marshall Trager , Shmuel Winograd
发明人： Charles Edwin Cox , Myron Dale Flickner , James Lee Hafner , Martin Aureliano Hassner , Barry Marshall Trager , Shmuel Winograd
IPC分类号： H03M13/00 , H03M13/15
CPC分类号： H03M13/1545 , H03M13/1515 , H03M13/616
摘要： A computationally efficient, machine-implementable method and means for detecting and correcting errors in received codewords on-the-fly within the capacity of a linear cyclic code using ultra-fast error location processing. Each error locator polynomial of degree t over a finite Galois field derived from a codeword syndrome is mapped into a matrix representative of a system of linear simultaneous equations related to the polynomial coefficients. Roots indicative of error locations within the codeword are extracted from the matrix by a modified Gaussian Elimination process for all the roots where t.ltoreq.5 and at least one root plus a subset of candidate roots from the finite field for iterative substitution where t>5. Corrected values are separately determined and correction is secured by logically combining the corrected values with the codeword values in error at the error locations represented by the roots.
摘要翻译：一种计算有效的机器可实现的方法和装置，用于使用超快速错误位置处理在线性循环码的容量内即时检测和纠正接收到的码字中的错误。将来自码字综合征的有限伽罗瓦域的度t的每个误差定位多项式映射成表示与多项式系数相关的线性联立方程组的矩阵。指示码字内的错误位置的根通过对于t 5的所有根的修正的高斯消除过程从矩阵中提取，并且至少一个根加上来自用于迭代取代的有限域的候选根的子集，其中t> 5。单独确定校正后的值，并且通过将修正的值与由根表示的错误位置处的错误的码字值进行逻辑组合来确保校正。

5. 发明授权

US06275965B1 Method and apparatus for efficient error detection and correction in long byte strings using generalized, integrated, interleaved reed-solomon codewords 失效
标题翻译：用于使用广义的，集成的，交错的簧片专用码字的长字节串中的有效误差检测和校正的方法和装置
公开(公告)号：US06275965B1
公开(公告)日：2001-08-14
申请号：US09260717
申请日：1999-03-01
申请人： Charles Edwin Cox , Martin Aureliano Hassner , Arvind Patel , Barry Marshall Trager
发明人： Charles Edwin Cox , Martin Aureliano Hassner , Arvind Patel , Barry Marshall Trager
IPC分类号： H03M1329
CPC分类号： G11B20/1833 , H03M13/1515 , H03M13/29 , H03M13/2903
摘要： A method and means for enhancing the error detection and correction capability obtained when a plurality of data byte strings are encoded in a two-level, block-formatted linear code using code word and block-level redundancy. This is accomplished by vector multiplication of N data byte vectors and a nonsingular invertible integration matrix with nonzero minors with order up to B to secure the necessary interleaving among N data byte vectors to form modified data byte vectors. The selected patterns of interleaving ensure single-pass, two-level linear block error correction coding when the modified data vectors are applied to an ECC encoding arrangement. The method and means are parameterized so as to either extend or reduce the number of bursty codewords or subblocks to which the block-level check bytes can be applied. Lastly, a post-encoding process is provided to “deinterleave” or redistribute the computed codewords into modified codewords such that the data vectors and their codeword check bytes are consistently located in the same codeword with the block-level check bytes are distributed among the first-level codewords.
摘要翻译：一种用于增强当使用代码字和块级冗余以两级块格式的线性代码编码多个数据字节串时获得的错误检测和校正能力的方法和装置。这是通过N个数据字节向量和非奇异可逆积分矩阵与非零未成年人的向量乘法来实现的，阶数达到B以在N个数据字节向量之间保证必要的交织以形成修改的数据字节向量。所选择的交织模式当将修改的数据向量应用于ECC编码装置时，确保单程，二级线性块纠错编码。该方法和装置被参数化，以便扩展或减少可应用块级检查字节的突发码字或子块的数量。最后，提供后编码处理以将所计算的码字“解交织”或重新分配为经修改的码字，使得数据向量及其码字校验字节一致地位于相同的码字中，其中块级校验字节分布在第一级代码字。

6. 发明授权

US06671850B1 On-the-fly algebraic error correction system and method for reducing error location search 有权
标题翻译：用于减少错误位置搜索的即时代数纠错系统和方法
公开(公告)号：US06671850B1
公开(公告)日：2003-12-30
申请号：US09562575
申请日：2000-05-01
申请人： Charles Edwin Cox , Martin Aureliano Hassner , Barry Marshall Trager , Shmuel Winograd
发明人： Charles Edwin Cox , Martin Aureliano Hassner , Barry Marshall Trager , Shmuel Winograd
IPC分类号： H03M1300
CPC分类号： H03M13/6502 , G06F7/724 , G06F2207/7209 , G11B20/1833 , H03M13/1525
摘要： An on-the-fly algebraic error correction system and corresponding method for reducing error location search are presented. The method transforms an error locator polynomial into two transformed polynomials whose roots are elements in a smaller subfield, in order to significantly simplify the complexity, and to reduce the latency of the error correcting system hardware implementation. More specifically, if the error locator polynomial is over a finite field of (22n) elements, the transformed polynomial is over a finite subfield of (2n) elements. Thus, the problem of locating the roots of the error locator polynomial is reduced to locating the roots of the transformed polynomials. Assuming the error locator polynomial is of degree m, the present method requires at most (m2/2) evaluations of polynomials over the Galois field GF(22n) and (2n+1) evaluations over the subfield GF(2n) or root finding of two polynomials of at most a degree m over the subfield GF(2n).
摘要翻译：提出了一种用于减少误差位置搜索的动态代数误差校正系统和相应的方法。该方法将误差定位多项式转换为两个变换多项式，其根是较小子场中的元素，以便显着简化复杂度，并减少纠错系统硬件实现的等待时间。更具体地说，如果误差定位多项式超过（2 <2n>）个元素的有限域，则变换多项式在（2 ）个元素的有限子场上。因此，定位错误定位多项式的根的问题减少到定位变换多项式的根。假设误差定位多项式为度数m，本方法在伽罗瓦域GF（2n）和（2

7. 发明授权

US06405339B1 Parallelized programmable encoder/syndrome generator 失效
标题翻译：并联可编程编码器/综合发生器
公开(公告)号：US06405339B1
公开(公告)日：2002-06-11
申请号：US09387665
申请日：1999-08-31
申请人： Charles Edwin Cox , Martin Aureliano Hassner
发明人： Charles Edwin Cox , Martin Aureliano Hassner
IPC分类号： G06F1110
CPC分类号： H03M13/159
摘要： A composite encoder/syndrome generating device that both computes check symbols over counterpart data symbol strings to form codewords, and derives syndromes from codewords indicative of their error state. The multistage device provides recursive processing paths at each stage of depth corresponding to the number of symbols concurrently applied to the device. The device is adapted as an encoder when the feed-forward paths between stages are enabled; it is adapted as a syndrome generator upon their disablement. The number of symbols concurrently processed may be varied from clock cycle to clock cycle by conforming the recursion paths per stage to the number of symbols applied as input to the device.
摘要翻译：复合编码器/校正子生成装置，其通过对应数据符号串计算校验符号以形成码字，并且从表示其错误状态的码字导出校正子。多级设备在与被同时应用于设备的符号数量相对应的深度的每个阶段提供递归处理路径。当启动级之间的前馈路径时，该设备适用于编码器; 它被禁用后适应为综合征发生器。通过将每个阶段的递归路径符合到作为输入到设备的输入的符号的数量，可以同时处理的符号的数目从时钟周期变化到时钟周期。

8. 发明授权

US6023782A RAM based key equation solver apparatus 失效
标题翻译：基于RAM的密钥方程求解器
公开(公告)号：US6023782A
公开(公告)日：2000-02-08
申请号：US766681
申请日：1996-12-13
申请人： Charles Edwin Cox , Martin Aureliano Hassner
发明人： Charles Edwin Cox , Martin Aureliano Hassner
IPC分类号： H03M13/15 , H03M13/00
CPC分类号： H03M13/158 , H03M13/1515
摘要： The present invention is a circuit for performing a computation of a plurality of coefficients of an error locator polynomial and a plurality of coefficients of an error evaluator polynomial in a system for correcting errors in a Reed-Solomon encoded datastream, comprising a syndrome generator outputting syndromes of the datastream. The circuit of the present invention is coupled to the syndrome generator and receives the syndromes. The present invention comprises an arithmetic unit iteratively generating intermediate and final values of the plurality of coefficients of an error locator polynomial and the plurality of coefficients of an error evaluator polynomial; a random access memory, storing the intermediate and final values of the plurality of coefficients of an error locator polynomial and the plurality of coefficients of an error evaluator polynomial; and a control unit, controlling the arithmetic unit and the memory and detecting when the computation of the plurality of coefficients of an error locator polynomial and the plurality of coefficients of an error evaluator polynomial has been completed.
摘要翻译：本发明是一种用于在Reed-Solomon编码数据流中用于校正错误的系统中执行误差定位多项式和多个系数的误差估计多项式的多个系数的计算的电路，其包括输出综合征的数据流。本发明的电路耦合到综合征发生器并接收综合征。本发明包括一个运算单元，迭代地产生误差定位多项式的多个系数和误差估计器多项式的多个系数的中间值和最终值; 存储错误定位多项式的多个系数的中间值和最终值以及误差评估器多项式的多个系数的随机存取存储器; 以及控制单元，控制运算单元和存储器，以及何时完成误差定位多项式的多个系数的计算和误差评估多项式的多个系数的计算。

9. 发明授权

US06792569B2 Root solver and associated method for solving finite field polynomial equations 失效
标题翻译：求解有限域多项式方程的根解和相关方法
公开(公告)号：US06792569B2
公开(公告)日：2004-09-14
申请号：US09842244
申请日：2001-04-24
申请人： Charles Edwin Cox , Martin Aureliano Hassner , Barry Marshall Trager , Shmuel Winograd
发明人： Charles Edwin Cox , Martin Aureliano Hassner , Barry Marshall Trager , Shmuel Winograd
IPC分类号： H03M1300
CPC分类号： H03M13/1545 , H03M13/1515
摘要： An error correction algebraic decoder uses a key equation solver for calculating the roots of finite field polynomial equations of degree up to six, and lends itself to efficient hardware implementation and low latency direction calculation. The decoder generally uses a two-step process. The first step is the conversion of quintic equations into sextic equations, and the second step is the adoption of an invertible Tschirnhausen transformation to reduce the sextic equations by eliminating the degree 5 term. The application of the Tschirnhausen transformation considerably decreases the complexity of the operations required in the transformation of the polynomial equation into a matrix. The second step defines a specific Gaussian elimination that separates the problem of solving quintic and sextic polynomial equations into a simpler problem of finding roots of a quadratic equation and a quartic equation.
摘要翻译：纠错代数解码器使用密钥方程求解器来计算六个有限域多项式方程的根，并适用于有效的硬件实现和低延迟方向计算。解码器通常采用两步法。第一步是将五次方程转换为性别方程，第二步是采用可逆的Tschirnhausen变换，通过消除5度项来减少性别方程。 Tschirnhausen变换的应用大大降低了将多项式方程转换为矩阵所需的操作的复杂性。第二步定义了一个特定的高斯消除，将解决五元和多项式多项式方程的问题分解成找到二次方程和四次方程的根的一个更简单的问题。

10. 发明授权

US6141786A Method and apparatus for performing arithmetic operations on Galois fields and their extensions 失效
标题翻译：用于对伽罗瓦域及其扩展进行算术运算的方法和装置
公开(公告)号：US6141786A
公开(公告)日：2000-10-31
申请号：US90511
申请日：1998-06-04
申请人： Charles Edwin Cox , Martin Aureliano Hassner , Barry Marshall Trager , Shmuel Winograd
发明人： Charles Edwin Cox , Martin Aureliano Hassner , Barry Marshall Trager , Shmuel Winograd
IPC分类号： H03M13/15 , G11C29/00
CPC分类号： H03M13/158 , H03M13/15 , H03M13/1515
摘要： The invention relates to an arithmetic unit (AU) in combination with an algebraic block ECC decoder for controlling errors in an electronically recorded digital data message by performing at least one of a plurality of predetermined arithmetic operations on the data message in one or more of a plurality of subfields of a first GF(2.sup.12) or a second GF(2.sup.8) finite field. The arithmetic operations are selected either from a first group of operations associated with a first subfield GF(2.sup.4) as cubically extended to the first finite field GF(2.sup.12) or as quadratically extended to the second finite field GF(2.sup.8), or selected from a second group of operations associated with a second subfield GF(2.sup.6) as quadratically extended to the first finite field GF(2.sup.12).
摘要翻译：本发明涉及一种与代数块ECC解码器组合的算术单元（AU），用于通过对数字消息中的一个或多个中的数据消息执行多个预定算术运算中的至少一个来控制电子记录数字数据消息中的错误，第一GF（212）或第二GF（28）有限域的多个子场。算术运算从与第一子场GF（24）相关联的第一组运算中选择为立方式扩展到第一有限域GF（212）或二次扩展到第二有限域GF（28），或从与第二子场GF（26）相关联的第二组操作，其被二次扩展到第一有限域GF（212）。

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