Low-cost methods and devices for the decoding of product cases

A decoding method, implemented by executing a program embedded in a computer readable medium, of decoding a product code, in which symbols of each codeword are 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 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 to be decoded by means of an algorithm A2 for correction with erasures, said method being characterized in that it comprises a succession of main steps which are implemented until the correction of the received word is complete, each of these steps consisting in processing either a row or a column of said table in a predetermined order, and in that it comprises, to process a row i (1≦i≦n2):

• a) applying the algorithm A1 to the row i taking into account the τ1i erased positions (if any),
• b) if the algorithm A1 is unable to correct the row, erasing all the symbols of that row,
• c) if the algorithm A1 is able to correct the row, counting the number t1i of symbols whose value has been changed during the correction in the row to be corrected and of which it was not known in advance that they were to be corrected, and determining whether the result of this correction is reliable on the basis of the value of t1i and of the number τ1i of erased symbols in this row and,
• if the result is deemed reliable, accepting said correction,
• if the result is not deemed reliable, erasing all the symbols of that row, and in that it comprises, to process a column j (1≦j≦n1):
• d) applying the algorithm A2 to the column j taking into account the τ2j erased positions (if any),
• e) if the algorithm A2 is unable to correct the column, erasing all the symbols of that column,
• f) if the algorithm A2 is able to correct the column, counting the number t2j of symbols whose value has been changed during the correction in the column to be corrected and of which it was not known in advance that they were to be corrected, and determining whether the result of this correction is reliable on the basis of the value of t2j and of the number τ2j of erased symbols in this column and,
• if the result is deemed reliable, accepting said correction,
• if the result is not deemed reliable, erasing all the symbols of that column.