Abstract:
A method for the encoding of a sequence of source words, the method comprising: a step for the selection of an encoding function to be applied to a source word to be encoded as a function of the content of said word to be encoded and of at least one preceding source word in said 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 said isolated binary element; and a step for the encoding of said word to be encoded implementing the selected encoding function.
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, 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.
Abstract:
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.
Abstract translation:在解码尺寸k和长度为n的一点代数几何代码的方法中,为了识别接收到的字中的错误的位置,定义尺寸(nk)×(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。 还讨论了适用于实现该方法的装置和装置。
Abstract:
In order to encode an original sequence of binary data (u), a first padding operation (508) is performed, supplementing the original sequence (u) so that the supplemented sequence (u) is divisible by a first divisor polynomial; a first recursive convolutional encoding operation (508) is performed, using the first divisor polynomial, encoding the supplemented original sequence (u); an interleaving operation (506) is performed, permuting the binary data in the original sequence (u) by means of a specific permutation, so as to obtain an interleaved sequence (u*); a second padding operation (510) is performed, supplementing the interleaved sequence (u*) so that the supplemented interleaved sequence (u*) is divisible by a second divisor polynomial (g2); and a second recursive convolutional encoding operation (510) is performed, using the second divisor polynomial, encoding the supplemented interleaved sequence (u*).
Abstract:
The encoding method to which the present invention relates takes into account a serial turbo-encoding having at least one permutation operation which retains the divisibility of polynomial representations of sequences by predetermined polynomials and a convolutional encoding operation which includes a division by such a predetermined polynomial.
Abstract:
A method of sending information includes sending, on a transmission channel, sequences of symbols. The sequences are of a fixed length that is not a multiple of 4 and are taken from a collection of sequences, at least three of which are orthogonal in pairs and such that any pair of sequences that is not orthogonal to each other comprises opposite sequences. The symbols are taken from an alphabet of non-nil integers.
Abstract:
The information coding device has: a first labeling means adapted to associate, with the information to be coded, K “initial” first degree polynomials, a coding means which performs a polynomial calculation: to form K “coded” sequences of P, greater than or equal to K, “coded” polynomials, the first being equal to one of the K initial polynomials and the others to the product of the preceding polynomial and a predetermined polynomial, and to form a “resultant” sequence of P “resultant” polynomials respectively equal to the sums of the coded polynomials of same rank of the K coded sequences, a second one-to-one labeling means adapted to label the points of a quadrature amplitude modulation signal constellation with the Q2 resultant polynomials, for two adjacent points of the constellation, the polynomials labeling them have one identical coefficient and the other coefficient differing only by 1 modulo Q, and a modulator for quadrature amplitude modulation.
Abstract:
A coding method for padding K information sequences ui (i=1, 2, . . . , K) to produce K+M1 binary sequences ai (i=1, 2, . . . , K) and ci (i=1, 2, . . . , M1) so that the sequences ai are divisible by a set of K predetermined generator polynomials gi(x) (i=1, 2, . . . , K) each dividing (XN0+1) and the M1 sequences ci are obtained in a calculation involving permutations of the sequences ai (i=1, 2, . . . , K); the permutations having the property of transforming a cyclic code of length N0 with generator polynomial gi(x) to an equivalent cyclic code with a predetermined generator polynomial gij(x).
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.