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1. 发明授权

US07134066B2 Generalized parity stripe data storage array 失效
标题翻译：广义奇偶条纹数据存储阵列
公开(公告)号：US07134066B2
公开(公告)日：2006-11-07
申请号：US10689814
申请日：2003-10-20
申请人： Martin Aureliano Hassner , Steven R. Hetzler , Tetsuya Tamura , Barry Marshall Trager , Shmuel Winograd
发明人： Martin Aureliano Hassner , Steven R. Hetzler , Tetsuya Tamura , Barry Marshall Trager , Shmuel Winograd
IPC分类号： G11C29/52 , G11C29/42
CPC分类号： H03M13/2909 , G06F11/1076 , H03M13/134 , H03M13/2906
摘要： The Hamming distance of an array of storage devices is increased by generating a parity check matrix based on column equations that are formed using an orthogonal parity code and includes a higher-order multiplier that changes each column. The higher order multiplier is selected to generate a finite basic field of a predetermined number of elements. The array has M rows and N columns, such that M is greater than or equal to three and N is greater than or equal to three. Row 1 through row M−2 of the array each have n–p data storage devices and p parity storage devices. Row M−1 of the array has n−(p+1) data storage devices and (p+1) parity storage devices. Lastly, row M of the array has N parity storage devices.
摘要翻译：存储装置阵列的汉明距离通过基于使用正交奇偶校验码形成的列方程生成奇偶校验矩阵而增加，并且包括改变每列的高阶乘法器。选择较高阶乘数以产生预定数量的元素的有限基本场。阵列具有M行和N列，使得M大于或等于3，N大于或等于3。阵列的行1至行M-2各自具有n-p个数据存储设备和p个奇偶校验存储设备。该阵列的行M-1具有n（p + 1）数据存储设备和（p + 1）奇偶校验存储设备。最后，数组的行M具有N个奇偶校验存储设备。

2. 发明授权

US07131052B2 Algebraic decoder and method for correcting an arbitrary mixture of burst and random errors 有权
标题翻译：代数解码器和校正任意混合脉冲串和随机误差的方法
公开(公告)号：US07131052B2
公开(公告)日：2006-10-31
申请号：US10217728
申请日：2002-08-12
申请人： Martin Aureliano Hassner , Tetsuya Tamura , Barry Marshall Trager , Shmuel Winograd
发明人： Martin Aureliano Hassner , Tetsuya Tamura , Barry Marshall Trager , Shmuel Winograd
IPC分类号： H03M13/03
CPC分类号： G11B20/1833
摘要： An error correction algebraic decoder and an associated method correct a combination of a B-byte burst of errors and t-byte random errors in a failed sector, by iteratively adding and removing an erasure (N−B) times until the entire failed sector has been scanned, provided the following inequality is satisfied: (B+2t)≦(R−1), where N denotes the number of bytes, B denotes the length of the burst of errors, t denotes the total number of random errors, and R denotes the number of check bytes in the failed sector. This results in a corrected sector at a decoding latency that is a generally linear function of the number of the check bytes R, as follows: Decoding Latency=5R(N−B).
摘要翻译：错误校正代数解码器和相关联的方法通过迭代地添加和去除擦除（NB）次直到整个故障扇区被扫描来校正错误扇区中的B字节突发和t字节随机错误的组合（B + 2t）<=（R-1），其中N表示字节数，B表示错误突发的长度，t表示随机误差的总数，R表示R 表示故障扇区中的校验字节数。这导致在解码延迟处的校正扇区，其是校验字节R的数量的大致线性函数，如下：解码延迟= 5R（N-B）。

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

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

5. 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。

6. 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。

7. 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）。

8. 发明授权

US06553536B1 Soft error correction algebraic decoder 失效
标题翻译：软错误校正代数解码器
公开(公告)号：US06553536B1
公开(公告)日：2003-04-22
申请号：US09611872
申请日：2000-07-07
申请人： Martin Aureliano Hassner , Richard Michael Hamilton New , Arvind Motibhai Patel , Tetsuya Tamura , Barry Marshall Trager
发明人： Martin Aureliano Hassner , Richard Michael Hamilton New , Arvind Motibhai Patel , Tetsuya Tamura , Barry Marshall Trager
IPC分类号： H03M1300
CPC分类号： H03M13/154 , H03M13/1515 , H03M13/45 , H03M13/455
摘要： A soft error correction algebraic decoder and an associated method use erasure reliability numbers to derive error locations and values. More specifically, symbol reliability numbers from a maximum likelihood (ML) decoder as well as a parity check success/failure from inner modulation code symbols are combined by a Reed-Solomon decoder in an iterative manner, such that the ratio of erasures to errors is maximized. The soft error correction (ECC) algebraic decoder and associated method decode Reed Solomon codes using a binary code and detector side information. The Reed Solomon codes are optimally suited for use on erasure channels. A threshold adjustment algorithm qualifies candidate erasures based on a detector error filter output as well as modulation code constraint success/failure information, in particular parity check or failure as current modulation codes in disk drive applications use parity checks. This algorithm creates fixed erasure inputs to the Reed Solomon decoder. A complementary soft decoding algorithm of the present invention teaches the use of a key equation solver algorithm that calculates error patterns obtained as a solution to a weighted rational interpolation problem with the weights given by the detector side information.
摘要翻译：软错误纠正代数解码器和相关方法使用擦除可靠性数字来导出错误位置和值。更具体地，来自最大似然（ML）解码器的符号可靠性数字以及来自内部调制码符号的奇偶校验成功/失败由Reed-Solomon解码器以迭代方式组合，使得擦除与误差的比率为最大化。软纠错（ECC）代数解码器和相关方法使用二进制码和检测器侧信息对Reed Solomon码进行解码。 Reed Solomon码最适合用于擦除通道。阈值调整算法基于检测器误差滤波器输出以及调制码约束成功/失败信息（特别是奇偶校验或故障）来限定候选擦除，因为磁盘驱动器应用中的当前调制码使用奇偶校验。该算法为Reed Solomon解码器创建固定的擦除输入。本发明的补码软解码算法教导了使用由检测器侧信息给出的权重来计算作为加权有理插值问题的解的方法获得的误差模式的密钥方程求解算法。

9. 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。

10. 发明授权

US06654924B1 System and method for error correction of digitized phase signals from MR/GMR head readback waveforms 失效
标题翻译：用于MR / GMR头回读波形数字化相位信号纠错的系统和方法
公开(公告)号：US06654924B1
公开(公告)日：2003-11-25
申请号：US09675857
申请日：2000-09-29
申请人： Martin Aureliano Hassner , Francesco Rezzi , Barry Marshall Trager
发明人： Martin Aureliano Hassner , Francesco Rezzi , Barry Marshall Trager
IPC分类号： H03M1300
CPC分类号： H03M13/095 , G11B20/1813 , H03M5/145 , H03M13/39
摘要： A system and method for algebraically correcting errors in complex digitized phase signals from a magneto-resistive or giant magneto-resistive (MR/GMR) head readback waveform includes a data state machine that encodes phase symbols into data bits in accordance with, e.g., the (1, 10) constraint and a parity state machine that generates parity symbols such that a single inserted parity symbol does not violate the (1, 7) constraint in a run length limited code and furthermore the data following the insertion will not violate the (1, 10) constraint in a run length limited code. The state machines can be used as a trellis to perform maximum likelihood decoding on received coded data, thus performing soft algebraic error detection on received data. The invention thus guarantees better overall error rate performance than hard decision post processing of blocks of detected bits by a parity check matrix which is otherwise vulnerable to loss of bit synchronization at high linear density recording.
摘要翻译：用于代数校正来自磁阻或巨磁阻（MR / GMR）磁头回读波形的复数数字相位信号中的误差的系统和方法包括：数据状态机，其将相位符号编码为数据位，例如，（1,10）约束和产生奇偶校验符号的奇偶校验状态机，使得单个插入的奇偶校验符号不违反游程长度限制代码中的（1,7）约束，此外，插入之后的数据将不会违反（ 1，10）在运行长度限制代码中的约束。状态机可以用作网格，对接收到的编码数据进行最大似然解码，从而对接收到的数据执行软代数误差检测。因此，本发明保证比通过奇偶校验矩阵的硬判决后处理检测到的比特的更好的总体错误率性能，否则在高线性密度记录时易于丢失比特同步。

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