Patent ID: 6370670
Filing Date: 2002-04-09
Classification: H03M

Abstract:
A coding method for the transmission of information representing a physical quantity in which, a set of K polynomials gi(x) (i=1, . . . , K), where K is a strictly positive integer, with binary coefficients of degree m and with a constant term equal to 1 having been predetermined, first of all said information is presented in the form of K binary sequences ui (i=1, . . . , K), of length (nâˆ’m), where n is the product of a predetermined strictly positive integer M by the integer N0 which is the smallest integer such that the polynomial (xN0+1) is divisible by all said polynomials gi(x), and then there is produced a set of (K+M1) binary sequences ai (i=1, . . . , K) and cj (j=1, . . . , M1), where M1 is an integer larger than 1, each of length n, intended to be transmitted and obtained as follows:one extends each sequence ui by means of m â€œpaddingâ€  bits to compute a sequence ai such that the polynomial ai (x) associated with ai is respectively divisible by gi (x), one generates sequences cj represented by the polynomials cj&it;(x)=&Sum;i=0K&it;aij*&it;(x)&it;fij&it;(x)/gij&it;(x),â€ƒwhere the gij(x) are predetermined polynomials which can be respectively equal to the polynomials gi(x), the fij(x) are predetermined polynomials having a degree at most equal to the degree of the respective polynomial gij(x), and the aij*(x) are KÂ·M1 polynomials representing binary sequences aij* each obtained by means of a predetermined permutation of the respective sequence ai, wherein at least one permuted sequence aij* is different from the corresponding sequence ai, and said permutations are chosen among the set of permutations which, in a representation where the binary data of each sequence ai are written, row by row, in a table with N0 columns and M rows, are the resultant of any number of so-called elementary permutations each of which: either has the property of transforming the cyclic code of length N0 and with a generator polynomial gi(x) into an equivalent cyclic code with a generator polynomial gij(x), and acts by permutation on the N0 columns of the table representing ai, or is any permutation of the symbols of a column of said table, which results in the fact that each polynomial aij*(x) is divisible by the respective polynomial gij(x).