Patents by Inventor Frédéric Lehobey
Frédéric Lehobey has filed for patents to protect the following inventions. This listing includes patent applications that are pending as well as patents that have already been granted by the United States Patent and Trademark Office (USPTO).
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Patent number: 7634711Abstract: 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.Type: GrantFiled: April 16, 2004Date of Patent: December 15, 2009Assignee: Canon Kabushiki KaishaInventors: Philippe Piret, Frédéric Lehobey
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Patent number: 7502988Abstract: 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.Type: GrantFiled: February 25, 2005Date of Patent: March 10, 2009Assignee: Canon Kabushiki KaishaInventors: Philippe Piret, Frédéric Lehobey, Philippe Le Bars
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Patent number: 7464323Abstract: 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.Type: GrantFiled: December 29, 2003Date of Patent: December 9, 2008Assignee: Canon Kabushiki KaishaInventors: Philippe Piret, Frédéric Lehobey, Philippe Le Bars, Frédérique Ehrmann-Patin
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Patent number: 7461329Abstract: A method of encoding information symbols comprises a step in which a word v, orthogonal to a matrix H, the element H?? of which is equal to the value taken by some monomial h?=YjXi at the point P? 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 h? 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.Type: GrantFiled: March 22, 2005Date of Patent: December 2, 2008Assignee: Canon Kabushiki KaishaInventors: Philippe Piret, Frédéric Lehobey, Philippe Le Bars
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Patent number: 7409629Abstract: 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 S? which has a line of index less than or equal to ? of which the elements are zero in the first w(?) columns. The invention also relates to devices and apparatuses adapted to implement this method.Type: GrantFiled: September 30, 2003Date of Patent: August 5, 2008Assignee: Canon Kabushiki KaishaInventors: Frédéric Lehobey, Philippe Piret
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Patent number: 7404134Abstract: 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.Type: GrantFiled: September 29, 2004Date of Patent: July 22, 2008Assignee: Canon Kabushiki KaishaInventors: Philippe Le Bars, Philippe Piret, Frédéric Lehobey
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Patent number: 7398456Abstract: The present invention concerns an encoding method in which encoding is performed of any information word a of length k in the form of a word ? belonging to a Reed-Solomon code C of dimension k? and length n? (with n??k?=n?k) such that the components of ?? situated in (n??n) arbitrary predetermined positions be systematically equal to respective predetermined constants (for example, all zero). The possibility then exists of deleting those components of fixed value to obtain a word ? of length n belonging to a code C, which thus constitutes a code that is shortened with respect to code C. The invention also relates to devices and apparatuses adapted to implement the encoding method. The invention may be used for encoding by means of an algebraic geometric code, when such encoding may be implemented by encoding by means of a plurality of shortened Reed-Solomon codes.Type: GrantFiled: July 21, 2004Date of Patent: July 8, 2008Assignee: Canon Kabushiki KaishaInventors: Philippe Piret, Philippe Le Bars, Frederic Lehobey
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Patent number: 7392454Abstract: 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.Type: GrantFiled: December 16, 2004Date of Patent: June 24, 2008Assignee: Canon Kabushiki KaishaInventors: Philippe Piret, Frédéric Lehobey, Philippe Le Bars
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Patent number: 7392461Abstract: 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 2?? in Z, where ? is a strictly positive integer and ? an integer greater than 1, obtained by taking the fiber product of ? component algebraic equations, each of said component equations governing the unknown X and an unknown Yi, where i=0, . . . , ??1, and being of degree 2? in Yi. This method comprises the decoding of 2(??1)? “clustered” codes, all defined on the same algebraic curve represented by one of said component equations.Type: GrantFiled: January 13, 2005Date of Patent: June 24, 2008Assignee: Canon Kabushiki KaishaInventors: Philippe Piret, Frédéric Lehobey, Philippe Le Bars
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Publication number: 20060227017Abstract: The present invention concerns an encoding method in which encoding is performed of any information word a of length k in the form of a word ? belonging to a Reed-Solomon code C of dimension k? and length n? (with n??k?=n?k) such that the components of ?? situated in (n??n) arbitrary predetermined positions be systematically equal to respective predetermined constants (for example, all zero). The possibility then exists of deleting those components of fixed value to obtain a word ? of length n belonging to a code C, which thus constitutes a code that is shortened with respect to code C. The invention also relates to devices and apparatuses adapted to implement the encoding method. The invention may be used for encoding by means of an algebraic geometric code, when such encoding may be implemented by encoding by means of a plurality of shortened Reed-Solomon codes.Type: ApplicationFiled: July 21, 2004Publication date: October 12, 2006Applicant: CANON KABUSHIKI KAISHAInventors: Philippe Piret, Philippe Le Bars, Frederic Lehobey
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Patent number: 7120850Abstract: 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.Type: GrantFiled: April 8, 2003Date of Patent: October 10, 2006Assignee: Canon Kabushiki KaishaInventors: Frédéric Lehobey, Philippe Piret
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Publication number: 20050257115Abstract: The present invention concerns a method of decoding a one-point algebraic geometric code defined on an algebraic curve represented by an equation in X and Z of degree 2?? in Z, where ? is a strictly positive integer and ? an integer greater than 1, obtained by taking the fiber product of ? component algebraic equations, each of said component equations governing the unknown X and an unknown Yi, where i=0, . . . , ??1, and being of degree 2? in Yi. This method comprises the decoding of 2(??1)? “clustered” codes, all defined on the same algebraic curve represented by one of said component equations. The invention also relates to devices and apparatuses adapted to implement this method.Type: ApplicationFiled: January 13, 2005Publication date: November 17, 2005Applicant: CANON KABUSHIKI KAISHAInventors: Philippe Piret, Frederic Lehobey, Philippe Le Bars
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Publication number: 20050210357Abstract: A method of encoding information symbols comprises a step in which a word v, orthogonal to a matrix H, the element H?? of which is equal to the value taken by some monomial h?=YjXi at the point P? of some locating set, is associated with every block of k information symbols belonging to a Galois field Fq. The invention shows how to choose the set of said monomials h? 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. The invention also relates to devices and apparatuses adapted to implement this method.Type: ApplicationFiled: March 22, 2005Publication date: September 22, 2005Applicant: CANON KABUSHIKI KAISHAInventors: Philippe Piret, Frederic Lehobey, Philippe Le Bars
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Publication number: 20050204268Abstract: 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, comprises, for any received word, a step of locating transmission errors affecting said received word. The correction of errors in said 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.Type: ApplicationFiled: February 25, 2005Publication date: September 15, 2005Applicant: CANON KABUSHIKI KAISHAInventors: Philippe Piret, Frederic Lehobey, Philippe Le Bars
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Publication number: 20050188291Abstract: In a method of 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. Devices and apparatuses adapted to implement this method are also discussed.Type: ApplicationFiled: December 16, 2004Publication date: August 25, 2005Applicant: CANON KABUSHIKI KAISHAInventors: Philippe Piret, Frederic Lehobey, Philippe Le Bars
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Publication number: 20050138533Abstract: 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.Type: ApplicationFiled: September 29, 2004Publication date: June 23, 2005Applicant: CANON KABUSHIKI KAISHAInventors: Philippe Le Bars, Philippe Piret, Frederic Lehobey
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Publication number: 20050015704Abstract: 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. The invention also concerns devices and apparatus intended to implement these coding and decoding methods.Type: ApplicationFiled: April 16, 2004Publication date: January 20, 2005Applicant: CANON KABUSHIKI KAISHAInventors: Philippe Piret, Frederic Lehobey
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Publication number: 20040194006Abstract: 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.Type: ApplicationFiled: December 29, 2003Publication date: September 30, 2004Applicant: CANON KABUSHIKI KAISHAInventors: Philippe Piret, Frederic Lehobey, Philippe Le Bars, Frederique Ehrmann-Patin
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Publication number: 20040117719Abstract: The present invention relates to a 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. According to the invention, matrices 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 S&lgr; which has a line of index less than or equal to &lgr; of which the elements are zero in the first w(&lgr;) columns. The invention also relates to devices and apparatuses adapted to implement this method.Type: ApplicationFiled: September 30, 2003Publication date: June 17, 2004Applicant: CANON KABUSHIKI KAISHAInventors: Frederic Lehobey, Philippe Piret
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Publication number: 20040039978Abstract: 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.Type: ApplicationFiled: April 8, 2003Publication date: February 26, 2004Applicant: Canon Kabushiki KaishaInventors: Frederic Lehobey, Philippe Piret