Abstract: 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.

Abstract: 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, includes calculating extended error syndromes (?j(i)) associated with a received word (r) and 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.

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: The invention relates to a method for transmitting a plurality of data packets to a receiver in a data communication system. The method comprises the steps of transmitting one or more data packets from a list of data packets to be transmitted (300); determining whether an acknowledgment is received for each transmitted data packet (301), and further comprises the following steps executed when it is determined at the determining step that an acknowledgement has not been received for at least one data packet, referred to as an unacknowledged data packet: selecting one or more additional data packets from the list of data packets to be transmitted (302); generating 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 (304); and transmitting at least one of the generated parity packets (305).

Abstract: 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.

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: 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.

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 (?j(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: 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.

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.

Abstract: 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.

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: 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.

Abstract: A method for encoding and decoding a sequence of words, corresponding signal, encoder, decoder, computer programs and storage means. A method for encoding a sequence of source words includes a step of selecting an encoding function to be applied to a source word to be encoded as a function of the content of the word to be encoded and of at least one preceding source word in the sequence so that the concatenation of two consecutive encoded words has no binary element, called an isolated binary element, sandwiched between two binary elements with a value different from that of the isolated binary element. The method further includes a step of encoding the word to be encoded implementing the selected encoding function.