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21. 发明授权

US5710782A System for correction of three and four errors 失效
标题翻译：用于校正三和四个错误的系统
公开(公告)号：US5710782A
公开(公告)日：1998-01-20
申请号：US580351
申请日：1995-12-28
申请人： Lih-Jyh Weng
发明人： Lih-Jyh Weng
IPC分类号： G11B20/18 , G06F7/72 , H03M13/00 , H03M13/15
CPC分类号： H03M13/151 , G06F7/724
摘要： A system determines the error locations of four errors in GF(2.sup.2m) by transforming a degree-four error locator polynomial ultimately into two quadratic equations, finding the solutions of these equations, and from these solutions determining the roots of an error locator polynomial. The system first manipulates the error locator polynomial, which is of the form: .sigma.(x)=.sigma..sub.4 x.sup.4 +.sigma..sub.3 x.sup.3 .sigma..sub.2 x.sup.2 +.sigma..sub.1 x+.sigma..sub.0 �1! into the form: .theta.(y)=y.sup.4 +.theta..sub.2 y.sup.2 +.theta..sub.1 y+.theta..sub.0 �2! where the .theta..sub.i 's are combinations of the coefficients of the terms of the error locator polynomial. The system has thus produced an equation in which the coefficient of the y.sup.3 term is 0. The system then factors .theta.(y), to produce .theta.(y)=(y.sup.2 +t*y+u)*(y.sup.2 +v*y+w), �3! where "*" represents multiplication. It then determines the values of t, u, v and w by equating the coefficients of the two expressions for .theta.(y) and solving first for the variable t, which is equal to v, and then for the variables w and u. Once the values of the variables are determined, the system solves two quadratic equations, one for each of the factors of equation 3. Based on these solutions, the system determines the four error locations associated with the degree-four error locator polynomial.
摘要翻译：系统通过将四度误差定位多项式最终转换成两个二次方程，找到这些方程的解，并从确定误差定位多项式的根的这些解决方案来确定GF（22m）中四个误差的误差位置。系统首先将错误定位多项式操作为：sigma（x）= sigma 4x4 + sigma 3x3 sigma 2x2 + sigma 1x + sigma 0 [1]形成：theta（y）= y4 + theta 2y2 + theta 1y + theta 0 [ 2]其中θi是误差定位多项式的项的系数的组合。因此，系统产生了一个方程，其中y3项的系数为0.然后，系统将θ（y）归因于θ（y）=（y2 + t * y + u）*（y2 + v * y + w），[3]其中“*”表示乘法。然后，通过将θ（y）的两个表达式的系数相等于等于v的变量t，然后对于变量w和u求解，来确定t，u，v和w的值。一旦确定变量的值，系统就可以求解两个二次方程，对于方程3的每一个因素，求解一个二次方程。根据这些解，系统确定与四度误差定位多项式相关联的四个误差位置。

22. 发明授权

US5521767A Optimized equalizer system for data recovery and timing extraction in partial response read channels 失效
标题翻译：优化的均衡器系统用于部分响应读通道中的数据恢复和定时提取
公开(公告)号：US5521767A
公开(公告)日：1996-05-28
申请号：US406834
申请日：1995-03-20
申请人： Lih-Jyh Weng , An-Loong Kok , Barry H. Gold
发明人： Lih-Jyh Weng , An-Loong Kok , Barry H. Gold
IPC分类号： G11B5/09 , G11B20/10 , H03L7/06 , H04L25/497 , G11B5/035 , H04L25/34
CPC分类号： G11B5/09 , G11B20/10009 , H03L7/06 , H04L25/497
摘要： A simplified architecture is provided for a partial response read channel. One digital equalizer is used in conjunction with a simple shaping circuit to minimize power consumption while concurrently optimizing both the data recovery and timing extraction functions.
摘要翻译：为部分响应读通道提供了简化的架构。一个数字均衡器与简单整形电路结合使用，以最小化功耗，同时优化数据恢复和定时提取功能。

23. 发明授权

US5428630A System and method for verifying the integrity of data written to a memory 失效
标题翻译：用于验证写入存储器的数据完整性的系统和方法
公开(公告)号：US5428630A
公开(公告)日：1995-06-27
申请号：US86528
申请日：1993-07-01
申请人： Lih-Jyh Weng , Bruce A. Leshay , Diana L. Langer
发明人： Lih-Jyh Weng , Bruce A. Leshay , Diana L. Langer
IPC分类号： G06F11/10 , H03M13/00
CPC分类号： G06F11/1008 , G06F11/1076
摘要： A method and system for verifying the integrity of data written to a mass memory medium. A local memory is directed by local memory control logic to store a data block that is received from a host microprocessor and that is to be written to the mass memory medium. The data block comprises a sequence of data symbols. An ECC encoder encodes the stored data block with error correction data. The error correction data comprises a sequence of error correction symbols that are appended to the data symbols. The data and error correction symbols are stored in the mass memory and immediately retrieved. An ECC decoder receives the retrieved data and error correction symbols from the mass memory and the data and error correction symbols of the encoded data block from the encoder. In response, the decoder generates an error status signal when more than a predetermined threshold number of the retrieved data and error correction symbols are improperly stored in the mass memory. The local memory control logic receives the error status signal and generates in response a second error status signal. The host microprocessor receives the second error status signal and generates in response remedial action signals.
摘要翻译：一种用于验证写入大容量存储介质的数据的完整性的方法和系统。本地存储器由本地存储器控制逻辑引导以存储从主微处理器接收并将被写入大容量存储介质的数据块。数据块包括数据符号序列。 ECC编码器对存储的数据块进行编码，并具有纠错数据。纠错数据包括附加到数据符号的纠错符号序列。数据和纠错符号存储在大容量存储器中并立即检索。 ECC解码器从编码器接收来自大容量存储器的检索数据和纠错符号以及编码数据块的数据和纠错符号。作为响应，当超过预定阈值数量的检索数据和纠错符号不正确地存储在大容量存储器中时，解码器产生错误状态信号。本地存储器控制逻辑接收错误状态信号并且响应地产生第二错误状态信号。主机微处理器接收第二错误状态信号并产生响应补救动作信号。

24. 发明授权

US5379305A Error correction system with selectable error correction capabilities 失效
标题翻译：纠错系统具有可选择的纠错能力
公开(公告)号：US5379305A
公开(公告)日：1995-01-03
申请号：US918208
申请日：1992-07-20
申请人： Lih-Jyh Weng
发明人： Lih-Jyh Weng
IPC分类号： G06F11/10 , H03M13/00 , H03M13/35
CPC分类号： H03M13/35
摘要： A single Reed-Solomon code is employed with modifications to allow information systems the freedom of selecting redundancy from 1 to R symbols, where R is the number of redundant symbols that the unmodified Reed-Solomon code employs. If P is the number of discarded redundancy symbols, then R-P redundancy symbols are retained, and the minimum distance of the modified code is 1+R-P. The system uses one of several alternative decoding schemes. One general scheme employs error-and-erasure decoding, and treats the P deleted symbols as erasures. Another general scheme operates directly on the shortened, modified code-word and modifies both the error syndromes and the error information derived from the syndromes to compensate for the deleted symbols.
摘要翻译：使用单个Reed-Solomon码进行修改以允许信息系统从1到R个符号中选择冗余的自由度，其中R是未修改的Reed-Solomon码所使用的冗余符号的数量。如果P是丢弃的冗余符号数，则保留R-P冗余符号，修改后的代码的最小距离为1 + R-P。该系统使用几种替代解码方案之一。一种一般方案采用错误和擦除解码，并将P删除的符号视为擦除。另一个通用方案直接在缩短的修改后的码字上进行操作，并修改错误综合征和从综合征导出的错误信息以补偿被删除的符号。

25. 发明授权

US5321703A Data recovery after error correction failure 失效
标题翻译：纠错后数据恢复失败
公开(公告)号：US5321703A
公开(公告)日：1994-06-14
申请号：US850718
申请日：1992-03-13
申请人： Lih-Jyh Weng
发明人： Lih-Jyh Weng
IPC分类号： G06F11/10 , G06F11/18 , G11C29/00 , H03M13/43 , H04L1/08
CPC分类号： G06F11/1044 , G06F11/10 , H03M13/43 , H04L1/08 , G06F11/187 , G06F2201/81 , G11C29/74
摘要： A method of data recovery in systems employing error-correction coding techniques is described. The technique may be used, for example, in conjunction with a data storage device or a data communications network. Several trials of accessing or transmitting the ECC-protected data are performed. The data from each trial is decoded, and is also saved. If none of the trials results in the successful decoding of the data, then a reconstruction function is employed to create a reconstructed version of the data from the sequence of data created by the trials. One method of reconstruction involves majority voting on a symbol-by-symbol basis. The reconstructed data created that way is then decoded in the same fashion as for each trial. A more powerful reconstruction function employs a threshold to determine whether each voted-on symbol is sufficiently "reliable". If not, it is marked as an erasure. The reconstructed data created by this reconstruction function is decoded according to an error-and-erasure algorithm, which increases the error-correcting power of the ECC.
摘要翻译：描述了采用纠错编码技术的系统中的数据恢复方法。该技术可以例如与数据存储设备或数据通信网络结合使用。执行访问或发送ECC保护数据的几个试验。来自每个试验的数据被解码，并且也被保存。如果没有一个试验导致数据的成功解码，则采用重建功能来从试验创建的数据序列中创建数据的重建版本。一种重建方法涉及到逐个符号的多数投票。然后以与每个试验相同的方式对创建的重建数据进行解码。更强大的重建功能采用阈值来确定每个投票符号是否足够“可靠”。如果没有，它被标记为擦除。根据错误和擦除算法对由该重构功能创建的重建数据进行解码，这增加了ECC的纠错能力。

26. 发明授权

US07278085B1 Simple error-correction codes for data buffers 有权
标题翻译：数据缓冲区的简单纠错码
公开(公告)号：US07278085B1
公开(公告)日：2007-10-02
申请号：US10608320
申请日：2003-06-27
申请人： Lih-Jyh Weng , Bruce Buch
发明人： Lih-Jyh Weng , Bruce Buch
IPC分类号： G11C29/00
CPC分类号： G11C7/1006 , G06F11/1008 , G11C2029/0411 , G11C2207/104
摘要： A method of and apparatus for handling errors occurring in data stored in memory is presented. Data to be stored in a buffer memory is applied to a generator matrix to generate parity check bits. The parity check bits are stored in the buffer memory along with the data. The stored data and parity check bits are read and the read data is used to regenerate the parity check bits. A result produced from the stored and regenerated parity check bits is usable to directly identify a location of an erroneous bit of the data in the buffer memory.
摘要翻译：提出了一种用于处理存储在存储器中的数据中出现的错误的方法和装置。要存储在缓冲存储器中的数据被应用于发生器矩阵以产生奇偶校验位。奇偶校验位与数据一起存储在缓冲存储器中。读取存储的数据和奇偶校验位，并且使用读取的数据来重新生成奇偶校验位。由存储和再生的奇偶校验位产生的结果可用于直接识别缓冲存储器中数据的错误位的位置。

27. 发明授权

US07085988B1 Hashing system utilizing error correction coding techniques 有权
标题翻译：利用纠错编码技术的哈希系统
公开(公告)号：US07085988B1
公开(公告)日：2006-08-01
申请号：US10393096
申请日：2003-03-20
申请人： Lih-Jyh Weng
发明人： Lih-Jyh Weng
IPC分类号： H03M13/00
CPC分类号： H04L9/0643 , H03M13/1505 , H03M13/19 , H04L2209/043 , H04L2209/12 , H04L2209/34
摘要： A hashing system produces hash values by manipulating n-bit sequences in accordance with a selected distance d error correction code (“ECC”) over an associated Galois Field. The current system produces a hash value for a given n-bit sequence by treating the sequence as either a corrupted n-bit ECC codeword or as “n” information bits of an (n+r)-bit ECC codeword. The hashing system may decode the n bits as a corrupted codeword of an (n, k, d) perfect ECC to produce an n-bit error-free codeword, and then use as the hash value the information bits of the error-free codeword. Alternatively, the hashing system may treat the n-bit sequence as a corrupted code word of a cyclic distance d ECC, and map the codeword to an (n−k)-bit “error pattern” that the system then uses as the hash value. The hashing system may instead treat the n-bit sequence as n “information” bits and encode the bits in accordance with an (n+r, n, d) ECC, to produce an r-bit hash value that consists of the associated redundancy bits.
摘要翻译：哈希系统通过在相关联的伽罗瓦域上根据所选择的距离d纠错码（“ECC”）操纵n比特序列来产生哈希值。当前系统通过将序列视为（n + r）位ECC码字的损坏的n位ECC码字或“n”个信息比特来产生给定的n比特序列的哈希值。哈希系统可以将n位解码为（n，k，d）完美ECC的损坏码字，以产生无位错的码字，然后用作无差错码字的信息比特的散列值。或者，散列系统可以将n位序列视为循环距离d ECC的损坏码字，并将码字映射到系统随后用作散列值的（n-k）位“错误模式”。哈希系统可以将n比特序列视为n个“信息”比特，并且根据（n + r，n，d）ECC对比特进行编码，以产生由相关冗余组成的r比特哈希值位。

28. 发明授权

US06968493B1 Randomizer systems for producing multiple-symbol randomizing sequences 失效
公开(公告)号：US06968493B1
公开(公告)日：2005-11-22
申请号：US09395845
申请日：1999-09-14
申请人： Lih-Jyh Weng
发明人： Lih-Jyh Weng
IPC分类号： H03M13/15 , H03M13/00 , H03M13/01 , H04L9/36
CPC分类号： H03M13/152 , G11B20/0021 , H03M13/00
摘要： A system that produces one or more non-repeating randomizer sequences of up to 2m−1 or more m-bit symbols includes a randomizer circuit that is set up in accordance with a polynomial with primitive elements of GF(2m) as coefficients. The system combines the randomizer sequence with all the symbols of ECC code words that are encoded using a BCH code over GF(2m) to produce a randomized code word. The particular primitive elements used and/or an initial state of one or more registers in the system specifies the particular sequence produced by the system. The initial state of each of the one or more registers is a selected one of the 2m−1 elements of GF(2m), and thus, 2m−1 different sequences may be produced by selecting a different initial state for a given one of the registers. If the coefficients are also selected from, for example, a set of “p” possible values, the system produces p*(2m−1) different sequences. The system may thus be used to encrypt the ECC code word by associating the code word with a particular selected initial state and/or coefficient. The coefficients may be selected to produce randomizer sequences that are predetermined minimum distances away from both the ECC code words.

29. 发明授权

US06493845B1 Parallel input output combined system for producing error correction code redundancy symbols and error syndromes 失效
标题翻译：并行输入输出组合系统，用于产生纠错码冗余符号和误差综合征
公开(公告)号：US06493845B1
公开(公告)日：2002-12-10
申请号：US09337122
申请日：1999-06-21
申请人： Ba-Zhong Shen , Lih-Jyh Weng , Diana L. Langer
发明人： Ba-Zhong Shen , Lih-Jyh Weng , Diana L. Langer
IPC分类号： H03M1300
CPC分类号： H03M13/6561 , H03M13/1515 , H03M13/158 , H03M13/6575
摘要： A parallel input/output combined encoding and syndrome generating system encodes two information symbols per clock cycle, and thereafter, produces two redundancy symbols per clock cycle. For an n-symbol code word with 2k information symbols cn−1, to cn−2k, the symbols cn−1, cn−3, cn−5 . . . are supplied, in turn, to a first input line while the symbols cn−2, cn−4, cn−6, . . . are supplied, in turn, to a second input line. In a first clock cycle, the symbol cn−1 is combined with the contents of the R registers, where R is the number of redundancy symbols, and the contents are multiplied by the respective roots of the generator polynomial. The products then are combined with the paired symbol cn−2 and the resulting sums are multiplied also by the roots of the generator polynomial. These products are then summed in a chain of R adders and the respective registers are appropriately updated with the results of the encoding of the two symbols. During the next clock cycle, the next pair of information symbols are encoded, with cn−3 supplied to the first input line and cn−4 supplied to the second input line, and so forth. During the kth clock cycle, when the last of the pairs of information symbols are being encoded, the system produces the first two redundancy symbols. The first redundancy symbol is the update value for the last register rR−1, and the system then manipulates the update value, to produce the second redundancy symbol in the same clock cycle. The pair of redundancy symbols are next fed back to the two input lines and encoded, as discussed above. For decoding, the chain of R feedback adders is broken, and each set of adders and multipliers operates separately to update the associated register with the results of the manipulation of two code word symbols per clock cycle.
摘要翻译：并行输入/输出组合编码和校正子生成系统每个时钟周期对两个信息符号进行编码，此后每个时钟周期产生两个冗余符号。对于具有2k个信息符号cn-1，到cn-2k的符号cn-1，cn-3，cn-5的n符号码字。。。依次被提供给第一输入线，而符号cn-2，cn-4，cn-6，...，。。依次被提供给第二输入线。在第一时钟周期中，符号cn-1与R寄存器的内容组合，其中R是冗余符号的数量，并且内容与生成多项式的各个根相乘。然后，产品与配对符号cn-2组合，并且所得到的和也乘以生成多项式的根。然后将这些产品加在R加法器链中，并且用两个符号的编码结果适当地更新相应的寄存器。在下一个时钟周期中，下一对信息符号被编码，cn-3被提供给第一输入线，cn-4被提供给第二输入线，等等。在第k个时钟周期期间，当最后一对信息符号被编码时，系统产生前两个冗余符号。第一冗余符号是最后一个寄存器rR-1的更新值，然后系统操作更新值，以在相同的时钟周期产生第二个冗余符号。如上所述，该对冗余符号被反馈到两条输入线并进行编码。对于解码，R反馈加法器的链路被破坏，并且每组加法器和乘法器单独操作以更新相关联的寄存器与每个时钟周期对两个码字符号的操纵的结果。

30. 发明授权

US06343367B1 Error correction system for five or more errors 有权
标题翻译：纠错系统出现五个或更多错误
公开(公告)号：US06343367B1
公开(公告)日：2002-01-29
申请号：US09277785
申请日：1999-03-29
申请人： Ba-Zhong Shen , Lih-Jyh Weng
发明人： Ba-Zhong Shen , Lih-Jyh Weng
IPC分类号： H03M1300
CPC分类号： H03M13/152 , H03M13/1515 , H03M13/158
摘要： An error correcting system for correcting “t” errors over GF(2m), where t is even and preferably greater than or equal to six, transforms the t-degree error locator polynomial c(x) into a polynomial t(x) in which at−1≈0, where ai is the coefficient of the xi term of the error locator polynomial and Tr(at−1)=1, where Tr(ai) is the trace of ai. The polynomial t(x) is factored into two factors, namely, one factor that is the greatest common divisor of t(x) and S ⁡ ( x ) = ∑ i = 0 m - 1 ⁢ x 2 i , and a second factor that is the greatest common divisor of t(x) and S(x)+1. The system determines the greatest common divisor of the polynomial and S(x) in two steps, first iteratively determining a residue R(x)≡S(x)mod t(x), and then calculating the greatest common divisor of t(x) and the lower-degree R(x). The system produces two factors of t(x), namely, g(x)=gcd(t(x), R(x)) and h ⁡ ( x ) = t ⁡ ( x ) g ⁡ ( x ) , and then determines the roots of the factors and transforms these roots into the roots of the error locator polynomial or, as necessary, continues factoring into factors of lower degree before determining the roots. When “t” is odd, the system represents the roots ri of the error locator polynomial as a linear combination of ri,k&bgr;k for k=0,1 . . . m−1, where ri,k&egr;GF(2) and &bgr;k is an element of a dual basis for GF(2m) over GF(2), and Tr(&agr;j&bgr;k) equals one when j=k and equals zero when jk. The rootsri are then ri=ri,0&bgr;0+ri,1&bgr;1+ . . . +ri,m−1&bgr;m−1 and Tr ⁡ ( α j ⁢ r i ) = ∑ k = 0 m - 1 ⁢ r i , k ⁢ Tr ⁡ ( α j ⁢ β k ) = r i , j The system next determines the greatest common divisor of the polynomial and S(&agr;jx) by iteratively determining Rj(x)≡S(&agr;jx)mod c(x), and then determining the greatest common divisor of c(x) and Rj(x). The system next determines two factors of c(x) as g(x)=gcd(c(x), Rj(x)) and h ⁡ ( x ) = t ⁡ ( x ) g ⁡ ( x ) and finds the roots of the two factors.
摘要翻译：用于校正GF（2m）上的“t”误差的纠错系统，其中t为偶数，优选大于或等于6，将t度误差定位多项式c（x）转换为多项式t（x），其中 at-1≈0，其中ai是误差定位多项式的xi项的系数，Tr（at-1）= 1，其中Tr（ai）是ai的轨迹。多项式t（x）被分解为两个因素，即作为t（x）的最大公约数的一个因子，以及作为t（x）和S（x）+1的最大公约数的第二因子。系统在两个步骤中确定多项式和S（x）的最大公约数，首先迭代确定残差R（x）= S（x）mod t（x），然后计算t（x）的最大公约数）和较低等级R（x）。系统产生t（x）的两个因子，即g（x）= gcd（t（x），R（x）），然后确定因子的根，并将这些根变换到误差定位多项式的根或者根据需要在确定根源之前继续考虑到较低程度的因素。当“t”为奇数时，系统将误差定位多项式的根ri代表为k = 0,1的ri，kbetak的线性组合。。。 m-1，其中ri，kepsiGF（2）和betak是在GF（2）上的GF（2m）的双重基础的元素，并且当j = k时Tr（alphajbetak）等于1，并且当jk等于零时。然后，系统然后系统通过迭代确定Rj（x）= S（alphajx）mod c（x）来确定多项式和S（alphajx）的最大公约数，然后确定c（x）的最大公约数和 Rj（x）。系统接下来将c（x）的两个因子确定为g（x）= gcd（c（x），Rj（x）），并找出两个因素的根源。

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