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    Method and device for coding and transmission using a sub-code of a product code
    31.
    发明授权
    Method and device for coding and transmission using a sub-code of a product code 失效
    使用产品代码的子代码进行编码和传输的方法和设备

    公开(公告)号：US06543021B1

    公开(公告)日：2003-04-01

    申请号：US09353155

    申请日：1999-07-14

    Applicant: Philippe Piret

    Inventor： Philippe Piret

    IPC: H03M1300

    CPC classification number: H03M13/2963 ,  H03M13/152 ,  H03M13/19 ,  H03M13/2717 ,  H03M13/2721

    Abstract: A method is provided for coding information representing a physical quantity and represented by first binary symbols, having an operation of calculating second binary symbols from the information, the second binary symbols being called calculated binary symbols and being provided in order to be disposed in a square table. For each calculated binary symbol, there exist at least three distinct diagonals in the table which contain this calculated binary symbol and which, deprived of this calculated binary symbol, still allow each one on its own to recalculate the calculated binary symbol. A coding device, a decoding method, a decoding device, a transmission method, and a transmission device are provided, as well as a camera, a facsimile machine, photographic apparatus, and a computer, implementing the invention.

    Abstract translation: 提供了一种用于编码表示物理量并由第一二进制符号表示的信息的方法，其具有从信息计算第二二进制符号的操作，第二二进制符号被称为计算的二进制符号，并且被提供以便被布置在正方形 表。 对于每个计算的二进制符号，在表中存在至少三个不同的对角线，其中包含该计算的二进制符号，并且被剥夺该计算的二进制符号仍然允许每个独立的对角线重新计算所计算的二进制符号。 提供了一种编码装置，解码方法，解码装置，传输方法和传输装置，以及实现本发明的照相机，传真机，照相装置和计算机。

    Coding and decoding methods and devices and equipment using them
    32.
    发明授权
    Coding and decoding methods and devices and equipment using them 失效
    编码和解码方法以及使用它们的设备和设备

    公开(公告)号：US06393065B1

    公开(公告)日：2002-05-21

    申请号：US09141589

    申请日：1998-08-28

    Applicant: Philippe Piret ,  Claude Le Dantec

    Inventor： Philippe Piret ,  Claude Le Dantec

    IPC: H04L512

    CPC classification number: H03M13/1515 ,  H03M13/251 ,  H03M13/611 ,  H04L1/0057

    Abstract: A coding device that supplied code words, the symbols of which are capable of modulating a physical quantity on a transmission channel making use of symbols of a first alphabet. The decoding of these words uses symbols of a second alphabet containing the first alphabet, the cardinal of the second alphabet being strictly greater than that of the first alphabet and not being an integer power of the cardinal of the first alphabet. The coding device has an input of the “primary” symbols belonging to the first alphabet, a processor which determines redundant symbols capable of allowing decoding of the code words formed from primary symbols and redundant symbols, by a decoder working on the second alphabet, and solves a system of equations expressing the constraints to be met so that the redundant symbols are in the first alphabet, and an output of the symbols of the code words.

    Abstract translation: 提供码字的编码装置，其符号能够利用第一字母表的符号来调制传输信道上的物理量。 这些字的解码使用包含第一字母表的第二字母表的符号，第二字母的基数严格地大于第一字母表的基数，而不是第一字母的基数的整数幂。 编码装置具有属于第一字母表的“主要”符号的输入，处理器，通过在第二字母表上工作的解码器来确定能够允许从主符号和冗余符号形成的码字的解码的冗余符号;以及 解决表达要满足的约束的等式的系统，使得冗余符号在第一字母表中，以及代码字的符号的输出。

    Data transmission method and devices
    34.
    发明授权
    Data transmission method and devices 失效
    数据传输方式和设备

    公开(公告)号：US6084918A

    公开(公告)日：2000-07-04

    申请号：US848617

    申请日：1997-04-29

    Applicant: Philippe Piret

    Inventor： Philippe Piret

    IPC: H04B1/707 ,  H04J13/00 ,  H04L27/34 ,  H04L23/02 ,  H03C3/00 ,  H04L27/36

    CPC classification number: H04L27/34

    Abstract: For each data element (symbol), a sequence of N points from a QAM constellation is transmitted. If the symbol period is T, then each point in the sequence may have a duration T/N. The sequence is determined by treating the constellation as a finite ring, and repeatedly multiplying the data point by a constant point.

    Abstract translation: 对于每个数据元素（符号），发送来自QAM星座的N个点的序列。 如果符号周期为T，则序列中的每个点可以具有持续时间T / N。 通过将星座视为有限环来确定序列，并且将数据点重复地乘以恒定点。

    Methods and devices for decoding one-point algebraic geometric codes
    36.
    发明授权
    Methods and devices for decoding one-point algebraic geometric codes 失效
    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

    Applicant: Frédéric Lehobey ,  Philippe Piret

    Inventor： Frédéric Lehobey ,  Philippe Piret

    IPC: H03M13/00

    CPC classification number: H03M13/132 ,  H03M13/15

    Abstract: 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.

    Abstract translation: 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。

    Encoding/decoding device using a reed-solomon encoder/decoder
    37.
    发明授权
    Encoding/decoding device using a reed-solomon encoder/decoder 失效
    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

    Applicant: Philippe Le Bars ,  Philippe Piret ,  Frédéric Lehobey

    Inventor： Philippe Le Bars ,  Philippe Piret ,  Frédéric Lehobey

    IPC: H03M13/13

    CPC classification number: H03M13/132 ,  G11B20/18 ,  H03M13/1515 ,  H03M13/153 ,  H03M13/154 ,  H03M13/155

    Abstract: 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.

    Abstract translation: 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）。

    Error locating methods and devices for algebraic geometric codes
    38.
    发明授权
    Error locating methods and devices for algebraic geometric codes 失效
    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

    Applicant: Philippe Piret ,  Frédéric Lehobey ,  Philippe Le Bars

    Inventor： Philippe Piret ,  Frédéric Lehobey ,  Philippe Le Bars

    IPC: H03M13/00

    CPC classification number: H03M13/132

    Abstract: 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.

    Abstract translation: 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。

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