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    Decoding Method for Algebraic Geometric Codes and Associated Device
    13.
    发明申请
    Decoding Method for Algebraic Geometric Codes and Associated Device 有权
    代数几何代码和相关设备的解码方法

    公开(公告)号：US20080270873A1

    公开(公告)日：2008-10-30

    申请号：US11722465

    申请日：2005-12-22

    Applicant: Philippe Piret ,  Philippe Le Bars

    Inventor： Philippe Piret ,  Philippe Le Bars

    IPC: H03M13/13

    CPC classification number: H03M13/132

    Abstract: The present invention relates to a method of decoding a one-point algebraic geometric code defined on an algebraic curve of type C(a,b) represented by an equation F(X,Y)=0 of degree b in X and of degree a in Y over Fq, comprising the following steps: —calculating extended error syndromes (σj(i)) associated with a received word (r); —determining the values of errors in each component (r(x, yp(x))) of the received word r, on the basis of the extended error syndromes calculated. Since the error value is determined for each component, it is not necessary to have recourse to an error locating step. The invention also relates to devices and apparatuses associated with the method.

    Abstract translation: 本发明涉及一种解码在由X的等级b的等式F（X，Y）= 0表示的类型C（a，b）的代数曲线上定义的一点代数几何码的方法， 包括以下步骤：计算与接收到的字（r）相关联的扩展错误综合征（sigma）（i））。 基于所计算的扩展误差综合征，确定接收到的字r的每个分量（r（x，y，p（x）））中的错误值。 由于为每个组件确定了错误值，因此无需追求错误定位步骤。 本发明还涉及与该方法相关联的装置和装置。

    Turbocoding methods with a large minimum distance, and systems for implementing them
    15.
    发明授权
    Turbocoding methods with a large minimum distance, and systems for implementing them 失效
    具有最小距离的Turbocoding方法以及实现它们的系统

    公开(公告)号：US06993698B2

    公开(公告)日：2006-01-31

    申请号：US09964657

    申请日：2001-09-28

    Applicant: Philippe Piret

    Inventor： Philippe Piret

    IPC: H03M13/29

    CPC classification number: H03M13/2996 ,  H03M13/23 ,  H03M13/2771

    Abstract: Turbocoding methods use a first RSC coder operating on sequences of binary data a, and a second RSC coder operating on binary sequences a* each obtained from a by means of a predetermined permutation. These permutations are designed so that, for any sequence a represented by a polynomial divisible by the recursion polynomial, the associated sequence a* is also represented by a polynomial divisible by the recursion polynomial. These permutations are relatively simple to implement, and are applicable to all the data sequences a which have a length which is a multiple of the period of the recursion polynomial. In addition, once the transfer functions of the coders and the sequence length have been chosen, it is possible to select, amongst the corresponding permutations, the one which will probably offer the highest minimum distance of the code. Application to devices and apparatus implementing these methods.

    Abstract translation: 涡轮编码方法使用在二进制数据序列（U STYLE =“SINGLE”）a上操作的第一RSC编码器，以及从 a * SINGLE“> a通过预定的排列。 这些排列被设计成使得对于由可由递归多项式除除的多项式表示的任何序列 a，相关联的序列 a *也由多项式表示，该多项式可以被 递归多项式。 这些排列实现起来相对简单，并且适用于所有的数据序列 a，其长度是递归多项式周期的倍数。 另外，一旦选择了编码器的传递函数和序列长度，就可以在相应的排列中选择可能提供代码最大最小距离的排列。 应用于实现这些方法的设备和设备。

    Decoding method and device and systems implementing them
    16.
    发明授权
    Decoding method and device and systems implementing them 失效

    公开(公告)号：US06910006B2

    公开(公告)日：2005-06-21

    申请号：US09892874

    申请日：2001-06-28

    Applicant: Philippe Piret

    Inventor： Philippe Piret

    IPC: G06F11/10 ,  H03M13/13 ,  H03M13/15 ,  H03M13/29 ,  H03M13/31 ,  G10L19/02

    CPC classification number: H03M13/2963 ,  H03M13/13 ,  H03M13/15 ,  H03M13/456

    Abstract: In order to decode a sequence α=(α1, . . . , αi, . . . , αn) where αi is the received electrical signal corresponding to a transmitted signal ai representing the ith binary element vi of a word v=(v1, . . . , vn) chosen in a code C of words satisfying v·hT=0, where h is a row n-tuplet on the set {0,1 }, whose number of 1 is denoted w, an item of extrinsic information ρext[A(i,h)]=P[ai=−1|A(i,h)]/P[ai=+1|A(i,h)] is determined on each of the elements vi covered by h, A(i,h) being the set of the received values αj covered by h, with the exception of αi, and P[ai|A(i,h)] being the probability that the ith signal transmitted was ai. This gives ρext[A(i,h)]=[S1(i)+S3(i)+ . . . ]/[1+S2(i)+S4(i)+ . . . ] where the numbers Sr(i) are calculated by applying the recurrence r - 1 ⁢ ∑ i = 1 w ⁢ z α i ⁢ S r - 1 ⁢ ( i ) - z α j ⁢ S r - 1 ⁢ ( j ) = S r ⁢ ( j ) to the numbers S0(i) initialised to 1, with z=exp(−4 E/N), where E is the energy of the transmitted signals ai and N is the spectral power density of the noise on the transmission channel.

    Device and method for transmitting information and device and method for receiving information
    18.
    发明授权
    Device and method for transmitting information and device and method for receiving information 失效
    用于发送信息的装置和方法以及用于接收信息的装置和方法

    公开(公告)号：US06560291B1

    公开(公告)日：2003-05-06

    申请号：US09277816

    申请日：1999-03-29

    Applicant: Philippe Piret ,  Claude Le Dantec

    Inventor： Philippe Piret ,  Claude Le Dantec

    IPC: H04L2700

    CPC classification number: H04J13/16 ,  H04L27/34

    Abstract: A method of transmitting information on a transmission channel associated with a first numerical alphabet that takes into account a matrix n×n with an orthogonal dominant H on a second numerical alphabet including at least three different non-null values, and a set of at least one sub-matrix of the matrix H, each sub-matrix of the set containing a number p greater than or equal to 2 rows of the matrix H. A sub-matrix from the set of sub-matrixes is selected along with a p-tuple of real numbers referred to as a “row of coefficients”, such that the matrix product of the row of coefficients and the selected sub-matrix supplies a sequence of numbers of the first alphabet, in order to represent the information to be transmitted. In addition to being orthogonal, matrix H is preferentially balanced.

    Abstract translation: 一种在与第一数字字母表相关联的传输信道上传送信息的方法，该方法在包括至少三个不同的非空值的第二数字字母表上考虑具有正交显性H的矩阵nxn，以及一组至少一个子 矩阵H的矩阵，集合的每个子矩阵包含大于或等于矩阵H的2行的数p。从子集合的子矩阵中选择一个子矩阵以及一个p元组 被称为“系数行”的实数，使得系列行和所选择的子矩阵的矩阵乘积提供第一字母表的数字序列，以便表示要发送的信息。 除正交之外，矩阵H优先平衡。

    Information transfer method and device, information receiving method and device and network stations using them
    19.
    发明授权
    Information transfer method and device, information receiving method and device and network stations using them 失效
    信息传输方法和设备，信息接收方法和设备以及使用它们的网络站

    公开(公告)号：US06421806B1

    公开(公告)日：2002-07-16

    申请号：US09464074

    申请日：1999-12-16

    Applicant: Philippe Piret

    Inventor： Philippe Piret

    IPC: H03M1315

    CPC classification number: H04L1/0057 ,  H04L1/0043 ,  H04L1/0052 ,  H04L27/3416

    Abstract: The information transfer method uses: an alphabet Z2t={0, 1, 2, . . . 2t−1}, t≧3, in which additions and multiplications are carried out modulo 2t, and a lifted Hamming code whose generator polynomial is in Z2t. It includes: coding (302) of the information by a sequence of words of the said code, labelling (303), each letter of the alphabet Z2t labelling a letter of an alphabet A, for two adjacent symbols of A, one of the labels is the residue modulo 2t of the other incremented by 1, for each word of the said code, transmission (305) of signals, a physical quantity of which is proportional to the elements of A labelled by each of the symbols of the words of the said code.

    Abstract translation: 信息传递方法使用：字母Z2t = {0,1,2，...， 。 。 2t-1}，t> = 3，其中以2t进行加法和乘法，并且生成生成多项式为Z2t的汉明码。其包括：通过所述信息的序列的序列对信息进行编码（302） 代码，标签（303），字母Z2t的每个字母标记字母A的字母，对于A的两个相邻符号，其中一个标签是另一个的2t的余数加1，对于所述 代码，传输（305）的信号，其物理量与由所述代码的单词的每个符号标记的A的元素成比例。

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