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1. 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。

2. 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

3. 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。

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

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）。

6. 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）。

7. 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。

8. 发明授权

US07350126B2 Method for constructing erasure correcting codes whose implementation requires only exclusive ORs 有权
标题翻译：用于构造擦除纠正码的方法，其执行仅需要异或
公开(公告)号：US07350126B2
公开(公告)日：2008-03-25
申请号：US10600593
申请日：2003-06-23
申请人： Shmuel Winograd , Barry Marshall Trager
发明人： Shmuel Winograd , Barry Marshall Trager
IPC分类号： H03M13/00
CPC分类号： G06F11/1076 , H03M13/134 , H03M13/1515 , H03M13/373 , H03M13/616 , H03M13/6569
摘要： Error correcting codes of any distance (including codes of distance greater than four) use only exclusive OR (XOR) operations. Any code over a finite field of characteristic two are converted into a code whose encoding and correcting algorithms involve only XORs of words (and loading and storing of the data). Thus, the implementation of the encoding and correcting algorithms is more efficient, since it uses only XORs of words—an operation which is available on almost all microprocessors. An important code, the (3, 3) code of distance four, is also described.
摘要翻译：任何距离（包括距离大于4的码）的纠错码仅使用异或（XOR）操作。特征2的有限域上的任何代码被转换成代码，其编码和校正算法仅涉及字的异或（并且加载和存储数据）。因此，编码和校正算法的实现更有效，因为它仅使用字的异或 - 几乎所有微处理器都可用的操作。还描述了一个重要的代码，即距离四的（3，3）代码。

9. 发明授权

US08171377B2 System to improve memory reliability and associated methods 有权
标题翻译：系统提高内存可靠性和相关方法
公开(公告)号：US08171377B2
公开(公告)日：2012-05-01
申请号：US12023374
申请日：2008-01-31
申请人： Timothy J. Dell , Luis A. Lastras-Montano , Barry M. Trager , Shmuel Winograd
发明人： Timothy J. Dell , Luis A. Lastras-Montano , Barry M. Trager , Shmuel Winograd
IPC分类号： G11C29/00
CPC分类号： H03M13/1545 , G06F11/1044 , H03M13/1515
摘要： A system to improve memory reliability in computer systems that may include memory chips, and may rely on a error control encoder to send codeword symbols for storage in each of the memory chips. At least two symbols from a codeword are assigned to each memory chip and therefore failure of any of the memory chips could affect two symbols or more. The system may also include a table to record failures and partial failures of the codeword symbols for each of the memory chips so the error control encoder can correct subsequent partial failures based upon the previous partial failures. The error control coder is capable of correcting and/or detecting more errors if only a fraction of a chip is noted in the table as having a failure as opposed to a full chip noted as having a failure.
摘要翻译：一种用于提高可能包括存储器芯片的计算机系统中的存储器可靠性的系统，并且可以依赖于错误控制编码器来发送用于存储在每个存储器芯片中的码字符号。来自码字的至少两个符号被分配给每个存储器芯片，因此任何存储器芯片的故障可能影响两个或更多个符号。该系统还可以包括用于记录每个存储器芯片的码字符号的故障和部分故障的表，因此错误控制编码器可以基于先前的部分故障来校正随后的部分故障。误差控制编码器能够校正和/或检测更多的误差，如果在表中只有一部分芯片被注意为具有故障，而不是被称为具有故障的全芯片。

10. 发明申请

US20080016413A1 RAID 3 + 3 有权
公开(公告)号：US20080016413A1
公开(公告)日：2008-01-17
申请号：US11747887
申请日：2007-05-11
申请人： Steven Hetzler , Daniel Smith , Shmuel Winograd
发明人： Steven Hetzler , Daniel Smith , Shmuel Winograd
IPC分类号： G06F11/00
CPC分类号： G06F11/1076 , G06F2211/1057 , G06F2211/1059 , G06F2211/1064
摘要： A data storage subsystem that includes three data storage units, three check storage units, and an array controller coupled to the three data and three check storage units can tolerate failure of any three data and check storage units failures can be occur before data stored on the data storage subsystem is lost. Information is stored on the data storage subsystem as a symmetric Maximum Distance Separation code, such as a Winograd code, a Reed Solomon code, an EVENODD code or a derivative of an EVENODD code. The array controller determines the contents of the check storage units so that any three erasures of the data storage units and the check storage units can be corrected by the array controller. The array controller updates a block of data contained in any one of the data storage units and the check storage units using only six IO operations.
摘要翻译：包含三个数据存储单元，三个检查存储单元和耦合到三个数据的阵列控制器和三个检查存储单元的数据存储子系统可以容忍任何三个数据的故障，并且检查存储单元可能在存储在数据存储子系统丢失。信息作为对称的最大距离分离码存储在数据存储子系统上，例如Winograd码，里德所罗门码，EVENODD码或EVENODD码的导数。阵列控制器确定检查存储单元的内容，使得数据存储单元和检查存储单元的任何三个擦除可以由阵列控制器校正。阵列控制器仅使用六个IO操作来更新包含在数据存储单元和检查存储单元中的任何一个中的数据块。

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