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1. 发明授权

US07502988B2 Decoding and error correction for algebraic geometric codes 失效
标题翻译：代数几何代码的解码和纠错
公开(公告)号：US07502988B2
公开(公告)日：2009-03-10
申请号：US11067067
申请日：2005-02-25
申请人： Philippe Piret , Frédéric Lehobey , Philippe Le Bars
发明人： Philippe Piret , Frédéric Lehobey , Philippe Le Bars
IPC分类号： H03M13/00
CPC分类号： H03M13/132 , H03M13/05 , H03M13/1515 , H03M13/1525
摘要： A method of decoding a one-point algebraic geometric code defined on an algebraic curve of the kind C(a,b), represented by an equation of degree b in X and of degree a in Y. For any received word, transmission errors affecting the received word are located. The correction of errors in the word, which belongs to an algebraic geometric code, is then reduced to the correction of errors in a certain number, at most equal to a, of words belonging to a Reed-Solomon code. Devices and apparatuses adapted to implement this method are also described.
摘要翻译：对由C类（a，b）的代数曲线定义的一点代数几何代码进行解码的方法，由X中的程度b的等式表示，并且在Y中为a度。对于任何接收到的字，影响传输错误收到的单词位于。然后将属于代数几何代码的单词中的错误的校正减少为属于里德 - 所罗门码的单词的一定数量，最多等于a的错误校正。还描述了适于实现该方法的装置和装置。

2. 发明授权

US07120850B2 Low-cost methods and devices for the decoding of product cases 失效
标题翻译：用于解码产品案例的低成本方法和设备
公开(公告)号：US07120850B2
公开(公告)日：2006-10-10
申请号：US10408458
申请日：2003-04-08
申请人： Frédéric Lehobey , Philippe Piret
发明人： Frédéric Lehobey , Philippe Piret
IPC分类号： H03M13/00
CPC分类号： H03M13/132 , G11B20/1813 , H03M13/1515 , H03M13/29 , H03M13/2909 , H03M13/293
摘要： A method of decoding product codes is disclosed, in which the symbols of each codeword may be placed in a table comprising n2 rows and n1 columns, such that the symbols constituting each row form a permitted word of length n1 according to a first component code able to be decoded by means of an algorithm A1 for correction with erasures, and the symbols constituting each column form a permitted word of length n2 according to a second component code able to be decoded by means of an algorithm A2 for correction with erasures. According to the method, a correction of a row or column is only accepted when the result of the correction is deemed reliable, otherwise all the symbols of that row or column are erased. Devices and apparatus adapted to implement this method are also disclosed. The method is preferably applied to algebraic geometric codes.
摘要翻译：公开了一种解码产品代码的方法，其中每个码字的符号可以被放置在包括n 2行和n 1列的表中，使得构成每行根据能够通过用于用擦除校正的算法A 1 1进行解码的第一分量代码形成长度为n <1的允许字，并且构成每个列根据能够通过用于用擦除校正的算法A 2被解码的第二分量代码形成长度为n 2的允许字。根据该方法，仅当校正结果被认为是可靠的时才接受行或列的校正，否则该行或列的所有符号被擦除。还公开了适用于实现该方法的装置和装置。该方法优选地应用于代数几何代码。

3. 发明授权

US07461329B2 Channel encoding adapted to error bursts 失效
标题翻译：通道编码适用于错误突发
公开(公告)号：US07461329B2
公开(公告)日：2008-12-02
申请号：US11085129
申请日：2005-03-22
申请人： Philippe Piret , Frédéric Lehobey , Philippe Le Bars
发明人： Philippe Piret , Frédéric Lehobey , Philippe Le Bars
IPC分类号： G06F11/00 , G08C25/00
CPC分类号： H03M13/132
摘要： A method of encoding information symbols comprises a step in which a word v, orthogonal to a matrix H, the element Hαβ of which is equal to the value taken by some monomial hα=YjXi at the point Pβ of some locating set, is associated with every block of k information symbols belonging to a Galois field Fq. The method chooses the set of monomials hα so as to define codes which can be decoded with an algorithm by aggregates of low complexity, and which provides a very good error correction capability, in particular for channels in which the errors tend to occur in bursts. Devices and apparatuses adapted to implement this method are also disclosed.
摘要翻译：编码信息符号的方法包括一个步骤，其中与矩阵H正交的单词，其元素Halphabeta等于在点Pbeta处的一些单项式Halpha = YjXi取的值某些定位集合与属于伽罗瓦域Fq的k个信息符号的每个块相关联。该方法选择一组单项式，以便定义可以通过低复杂度聚合的算法解码的代码，并且其提供非常好的纠错能力，特别是对于其中错误倾向于在突发中发生的信道。还公开了适于实现该方法的装置和装置。

4. 发明授权

US07409629B2 Methods and devices for decoding one-point algebraic geometric codes 失效
标题翻译：用于解码一点代数几何代码的方法和装置
公开(公告)号：US07409629B2
公开(公告)日：2008-08-05
申请号：US10673288
申请日：2003-09-30
申请人： Frédéric Lehobey , Philippe Piret
发明人： Frédéric Lehobey , Philippe Piret
IPC分类号： H03M13/00
CPC分类号： H03M13/132 , H03M13/15
摘要： A method of decoding a one-point algebraic geometric code of dimension k and length n, in which, in order to identify the position of the errors in a received word, the syndromes matrix S, of size (n−k)×(n−k), is defined, of which the elements Sij of each line i are calculated, for j between 1 and w(i), where the boundary w is a decreasing function, using the syndrome s of the received word. Matrices Su are constructed for the successive values of u starting with S1=S, and, for u>1, each matrix Su is obtained by performing on the matrix Su−1, column permutations where appropriate, then linear manipulations involving the line of index u. These steps are performed in such a manner as to find a matrix Sλ which has a line of index less than or equal to λ of which the elements are zero in the first w(λ) columns. The invention also relates to devices and apparatuses adapted to implement this method.
摘要翻译：解码尺寸k和长度n的一点代数几何代码的方法，其中为了识别接收到的字中的错误的位置，大小（nk）×（nk）的校正子矩阵S 被定义为对于i和w（i）之间的j来计算每行i的元素S ij ij，其中边界w是递减函数，使用综合征。对于从S 1> S开始的u的连续值，构造矩阵S U，并且对于u> 1，每个矩阵S 是通过在适当的情况下执行矩阵S u-1>列排列而获得的，然后是涉及索引u的线的线性操作。以这样的方式执行这些步骤，以便找到在第一w（lambda）列中元素为零的索引小于或等于λ的行的矩阵S 。本发明还涉及适于实现该方法的装置和装置。

5. 发明授权

US07404134B2 Encoding/decoding device using a reed-solomon encoder/decoder 失效
标题翻译：使用芦苇编码器/解码器的编码/解码装置
公开(公告)号：US07404134B2
公开(公告)日：2008-07-22
申请号：US10952597
申请日：2004-09-29
申请人： Philippe Le Bars , Philippe Piret , Frédéric Lehobey
发明人： Philippe Le Bars , Philippe Piret , Frédéric Lehobey
IPC分类号： H03M13/13
CPC分类号： H03M13/132 , G11B20/18 , H03M13/1515 , H03M13/153 , H03M13/154 , H03M13/155
摘要： The present invention concerns a device (10) for the encoding of information symbols to transmit or to record, and for the correction of errors among the symbols received or read, according to codes defined over a Galois field Fq, where q is an integer greater than 2 and equal to a power of a prime number, and in which a set of elements of Fq are considered which are denoted yl(j), where j=1, . . . , R with 1≦R≦q−1 and l=0, . . . , p−1 with p>1. Said device (10) comprises a Reed-Solomon encoder (210), a Reed-Solomon decoder (220) and a unit (500) serving to calculate the inverse of a Vandermonde matrix as well as: registers “A” (420, 430, 440, 450) in which are stored, for the encoding, said information symbols, and, for the error correction, the symbols received or read after they have been corrected, registers “S” (280, 285, 290, 295) in which are stored, for the encoding, the symbols output from said Reed-Solomon encoder (210), and, for the error correction, the symbols entering said Reed-Solomon decoder (220), and registers “Y” (410, 411, 412, 413) in which said quantities yl(j) are stored.
摘要翻译：本发明涉及一种用于编码信息符号的设备（10），用于根据Galois域F 中定义的代码对接收或读取的符号进行传输或记录以及纠正错误的信息符号 >，其中q是大于2并且等于素数的幂的整数，并且其中考虑了一组表示为Q 1的元素的集合。 >（j），其中j = 1。。。，R 1具有1≤R= q-1且l = 0。。。，p-1，p> 1。所述设备（10）包括Reed-Solomon编码器（210），Reed-Solomon解码器（220）和用于计算Vandermonde矩阵的逆的单元（500），以及寄存器“A”（420,430 ，440,450），其中存储有用于编码所述信息符号的数据，并且对于在纠正之后接收或读取的符号进行纠错，将“S”（280,285,290,295）注册在用于编码从所述里德 - 所罗门编码器（210）输出的符号，以及对于进入所述里德 - 所罗门解码器（220）的符号进行纠错，并将“Y”（410,411,411） 412，413），其中存储所述数量Y 1（j）。

6. 发明授权

US07392454B2 Error locating methods and devices for algebraic geometric codes 失效
标题翻译：定位代数几何代码的方法和设备出错
公开(公告)号：US07392454B2
公开(公告)日：2008-06-24
申请号：US11012092
申请日：2004-12-16
申请人： Philippe Piret , Frédéric Lehobey , Philippe Le Bars
发明人： Philippe Piret , Frédéric Lehobey , Philippe Le Bars
IPC分类号： H03M13/00
CPC分类号： H03M13/132
摘要： Method and apparatus for decoding a one-point algebraic geometric code of dimension k and length n, in order to identify the position of the errors in a received word, the syndromes matrix S, of dimension (n−k)×(n−k) is defined, of which the elements Sij of each line i are calculated, for j between 1 and w(i), where the boundary w is a decreasing function, using the syndrome s of the received word, as well as the matrix S* obtained by “extending” the matrix S, that is to say by calculating the value of certain elements S*ij where j is greater than w(i). This method makes it possible in certain favorable cases to find the erroneous positions of the received word when the number of errors is greater than (n−k+1−g)/2, even if it is not possible to calculate all the elements of S* conventionally required by a two-stage algorithm to perform that correction.
摘要翻译：为了识别接收到的字中的错误的位置，对尺寸k和长度n的一点代数几何码进行解码的方法和装置，定义尺寸（nk）x（nk）的校正矩阵S，对于i和w（i）之间的j，计算每行i的元素S ij ij，其中边界w是递减函数，使用综合征 s，以及通过“扩展”矩阵S而获得的矩阵S *，也就是说通过计算某些元素S * 其中j大于w的值一世）。该方法使得当误差数大于（n-k + 1-g）/ 2时，在某些有利的情况下可以发现接收字的错误位置，即使不可能计算出所有元素的全部元素 S *通常由两级算法执行该校正所要求的。

7. 发明授权

US07634711B2 Information coding by algebraic geometric code offering two decoding options 失效
标题翻译：通过代数几何代码提供信息编码，提供两种解码选项
公开(公告)号：US07634711B2
公开(公告)日：2009-12-15
申请号：US10825283
申请日：2004-04-16
申请人： Philippe Piret , Frédéric Lehobey
发明人： Philippe Piret , Frédéric Lehobey
IPC分类号： H03M13/00
CPC分类号： H04L1/0041 , H03M13/132 , H03M13/15 , H03M13/151 , H03M13/27 , H03M13/353 , H03M13/356 , H03M13/6312 , H04L1/0045 , H04L1/0057 , H04L1/0071
摘要： The present invention concerns a method of coding information symbols according to a code defined on a Galois field Fq, where q is an integer greater than 2 and equal to a power of a prime number, and of length n=p(q−1), where p>1. This coding is designed so that there exists a corresponding decoding method, also disclosed by the invention, in which the correction of transmission errors essentially comes down to the correction of errors in p words of length (q−1) coded according to Reed-Solomon. The invention is particularly advantageous when, through a suitable choice of parameters, the code according to the invention is an algebraic geometric code: in this case, it is possible to correct the transmission errors by the method already mentioned and/or by a conventional method which is less economical but has a higher performance.
摘要翻译：本发明涉及一种根据在伽罗瓦域Fq上定义的代码对信息符号进行编码的方法，其中q是大于2且等于质数的幂的整数，并且长度为n = p（q-1），其中p> 1。该编码被设计成使得存在本发明也公开的对应的解码方法，其中传输错误的校正基本上归结于根据Reed-Solomon编码的长度（q-1）的p个字的错误的校正。当通过合适的参数选择，根据本发明的代码是代数几何代码时，本发明是特别有利的：在这种情况下，可以通过已经提及的方法和/或通过常规方法来校正传输错误这是较不经济但具有较高的性能。

8. 发明授权

US07464323B2 Algebraic geometric code adapted to error bursts 失效
标题翻译：适用于错误突发的代数几何代码
公开(公告)号：US07464323B2
公开(公告)日：2008-12-09
申请号：US10746144
申请日：2003-12-29
申请人： Philippe Piret , Frédéric Lehobey , Philippe Le Bars , Frédérique Ehrmann-Patin
发明人： Philippe Piret , Frédéric Lehobey , Philippe Le Bars , Frédérique Ehrmann-Patin
IPC分类号： H03M13/00
CPC分类号： H03M13/132 , H03M13/17
摘要： The present invention concerns channel codes particularly well adapted to transmission in channels in which errors tend to occur in bursts. Moreover, the codes according to one embodiment of the invention using an algebraic geometric curve are easy to decode and have a relatively high minimum distance. The invention also relates to the corresponding encoding and decoding methods, as well as the devices and apparatuses adapted to implement those methods. Application is in particular to mass storage, and to systems of communication by OFDM.
摘要翻译：本发明涉及特别适用于其中在突发中倾向于发生错误的信道中的传输的信道码。此外，根据使用代数几何曲线的本发明的一个实施例的代码易于解码并且具有相对较高的最小距离。本发明还涉及相应的编码和解码方法以及适于实现这些方法的装置和装置。应用特别是大容量存储，以及通过OFDM的通信系统。

9. 发明授权

US07392461B2 Decoding for algebraic geometric code associated with a fiber product 失效
标题翻译：解码与纤维产品相关联的代数几何代码
公开(公告)号：US07392461B2
公开(公告)日：2008-06-24
申请号：US11034009
申请日：2005-01-13
申请人： Philippe Piret , Frédéric Lehobey , Philippe Le Bars
发明人： Philippe Piret , Frédéric Lehobey , Philippe Le Bars
IPC分类号： H03M13/00
CPC分类号： H03M13/132
摘要： The present invention concerns a method and apparatus of decoding a one-point algebraic geometric code defined on an algebraic curve represented by an equation in X and Z of degree 2μφ in Z, where φ is a strictly positive integer and μ an integer greater than 1, obtained by taking the fiber product of μ component algebraic equations, each of said component equations governing the unknown X and an unknown Yi, where i=0, . . . , μ−1, and being of degree 2φ in Yi. This method comprises the decoding of 2(μ−1)φ “clustered” codes, all defined on the same algebraic curve represented by one of said component equations.
摘要翻译：本发明涉及一种解码在由Z中的程度2 Muphi 的X和Z表示的代数曲线上定义的一点代数几何代码的方法和装置，其中phi是严格正数通过获取μ分量代数方程的纤维积，通过控制未知X的每个组分方程和其中i = 0的未知Y i i，得到整数和μa大于1的整数。。。，mu-1，并且在YII中具有2级的phi 。该方法包括对由所述分量方程之一表示的相同代数曲线上定义的2（μ-1）个“聚集”码的解码。本发明还涉及适于实现该方法的装置和装置。

10. 发明授权

US08386901B2 Method, device and software application for transmitting data packets in a communication system 失效
标题翻译：用于在通信系统中传输数据分组的方法，设备和软件应用
公开(公告)号：US08386901B2
公开(公告)日：2013-02-26
申请号：US12441101
申请日：2007-09-26
申请人： Philippe Piret , Philippe Le Bars , Julien Sevin-Renault
发明人： Philippe Piret , Philippe Le Bars , Julien Sevin-Renault
IPC分类号： G06F11/00
CPC分类号： H04L1/1819 , H04L69/16 , H04L69/163
摘要： A transmitting apparatus transmits a plurality of data packets to a receiver in a communication system, by transmitting one or more data packets from a list of data packets to be transmitted, and determining whether an acknowledgment is received for each transmitted data packet. When it is determined that an acknowledgement has not been received for at least one data packet, referred to as an unacknowledged data packet, the apparatus selects one or more additional data packets from the list of data packets to be transmitted, generates one or more parity packets by encoding a block of data containing a combination of the selected one or more additional data packets and at least one unacknowledged data packet using a forward error correction scheme, and transmits at least one of the generated parity packets.
摘要翻译：发送装置通过从要发送的数据分组的列表发送一个或多个数据分组，并且确定是否为每个发送的数据分组接收到确认，在通信系统中向接收机发送多个数据分组。当确定至少一个称为未确认数据分组的数据分组的确认尚未被接收时，该装置从要发送的数据分组列表中选择一个或多个附加数据分组，产生一个或多个奇偶校验通过使用前向纠错方案对包含所选择的一个或多个附加数据分组的组合的数据块和至少一个未确认的数据分组进行编码来发送分组，并且发送所生成的奇偶分组中的至少一个。

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