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    Method and device for the correction of errors in the transmission of series of information items
    51.
    发明授权
    Method and device for the correction of errors in the transmission of series of information items 失效
    用于纠正传输系列信息项目中的错误的方法和装置

    公开(公告)号：US5867508A

    公开(公告)日：1999-02-02

    申请号：US840820

    申请日：1997-04-16

    Applicant: Philippe Piret

    Inventor： Philippe Piret

    IPC: H03M7/14 ,  H04B14/04 ,  H04L1/00 ,  H03M13/00

    CPC classification number: H04L1/0054 ,  H04L1/0041

    Abstract: According to the invention, for the transmission of sequences of information items referred to as "code words", among which sequences referred to as "operative words" are selected, on reception of a signal representing received words, each formed from a sequence of numbers having one of at least three values, and representing a code word, the following are implemented: a function of combining two sequences, one of which is an operative word, the said combination providing a so-called "resultant" sequence; a measurement whereby there is made to correspond to each sequence a real number representing the degree of coherence of the sequence; and, for each word received; at least one sequence resulting from the said received word and from an operative word is calculated iteratively and the said received word is replaced by the said resultant sequence from the moment when the measurement of the degree of coherence of the latter indicates a coherence less than that of the received word, this resultant sequence being referred to as a "replacement sequence", until no new combination of the last replacement sequence with any operative word exhibits a degree of coherence whose measurement is less than that of the said last replacement sequence,; the said last replacement sequence then being considered as representing the difference between the word received and the code word which it represents.

    Abstract translation: 根据本发明，对于被称为“代码字”的信息项的序列的传输，其中选择了称为“操作字”的序列，在接收到表示接收到的字的信号时，每个由数字序列形成 具有至少三个值中的一个并且表示码字，实现以下功能：组合两个序列的功能，其中一个是一个操作字，所述组合提供所谓的“结果”序列; 这样做的测量结果使得与每个序列相对应的表示序列一致性的实数; 对于收到的每一个字; 从所述接收到的字和从操作字产生的至少一个序列被迭代地计算，并且从后者的相干程度的测量指示相干度的相关性小于那一点的时刻，所述接收到的字被所述结果序列替换。 将所得到的序列称为“替换序列”，直到最后一个替换序列与任何手术词的新组合不存在其测量值小于所述最后替换序列的相干程度; 所述最后一个替换序列然后被认为表示所接收的字与其表示的码字之间的差异。

    Information coding by algebraic geometric code offering two decoding options
    59.
    发明授权
    Information coding by algebraic geometric code offering two decoding options 失效
    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

    Applicant: Philippe Piret ,  Frédéric Lehobey

    Inventor： Philippe Piret ,  Frédéric Lehobey

    IPC: H03M13/00

    CPC classification number: H04L1/0041 ,  H03M13/132 ,  H03M13/15 ,  H03M13/151 ,  H03M13/27 ,  H03M13/353 ,  H03M13/356 ,  H03M13/6312 ,  H04L1/0045 ,  H04L1/0057 ,  H04L1/0071

    Abstract: 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.

    Abstract translation: 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。

    Algebraic geometric code adapted to error bursts
    60.
    发明授权
    Algebraic geometric code adapted to error bursts 失效
    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

    Applicant: Philippe Piret ,  Frédéric Lehobey ,  Philippe Le Bars ,  Frédérique Ehrmann-Patin

    Inventor： Philippe Piret ,  Frédéric Lehobey ,  Philippe Le Bars ,  Frédérique Ehrmann-Patin

    IPC: H03M13/00

    CPC classification number: H03M13/132 ,  H03M13/17

    Abstract: 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.

    Abstract translation: 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。

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