A method for decoding a codeword, said codeword being obtained by implementing a code comprising at least one non-binary constraint node C over a set S of cardinality q > 2 defined from a parity check matrix H C of the non-binary constraint node C by the equation H C . ( p 1 ( V 1 ) , p 2 ( V 2 ) , ... , p d c ( V d c )) T = 0, where V 1 , V 2 , ... , V d c are a sub-set of non-binary variable nodes of the codeword implied in the non-binary constraint node C, with d c > 2 the degree of connectivity of the non-binary constraint node C and p 1 , p 2 , ... p d c are permutations over the set S, wherein said decoding method implements, for at least one connection between the non-binary variable node V j , 1 ≤ j ≤ d c , and the non-binary constraint node C, at least one decoding iteration comprising sending a message from the non-binary constraint node C to the non-binary variable node V j , said message comprising: - n R measures of reliability obtained for n R candidate symbols selected by the non-binary variable node V j or by a first compression block implemented between the non-binary variable node V j and the non-binary constraint node C, said n R candidate symbols being denoted n R requested symbols, - n B measures of reliability obtained for n B candidate symbols selected by the non-binary constraint node C or by a second compression block implemented between the non-binary constraint node C and the non-binary variable node V j , said n B candidate symbols being denoted n B best symbols, with 1 ≤ n B < q, 1 ≤ n R < q and n R + n B < q. said codeword being obtained by implementing a code comprising at least one non-binary constraint node C over a set S of cardinality q > 2 defined from a parity check matrix H C of the non-binary constraint node C by the equation H C . ( p 1 ( V 1 ) , p 2 ( V 2 ) , ... , p d c ( V d c )) T = 0, where V 1 , V 2 , ... , V d c are a sub-set of non-binary variable nodes of the codeword implied in the non-binary constraint node C, with d c > 2 the degree of connectivity of the non-binary constraint node C and p 1 , p 2 , ... p d c are permutations over the set S, wherein said decoding method implements, for at least one connection between the non-binary variable node V j , 1 ≤ j ≤ d c , and the non-binary constraint node C, at least one decoding iteration comprising sending a message from the non-binary constraint node C to the non-binary variable node V j , said message comprising: - n R measures of reliability obtained for n R candidate symbols selected by the non-binary variable node V j or by a first compression block implemented between the non-binary variable node V j and the non-binary constraint node C, said n R candidate symbols being denoted n R requested symbols, - n B measures of reliability obtained for n B candidate symbols selected by the non-binary constraint node C or by a second compression block implemented between the non-binary constraint node C and the non-binary variable node V j , said n B candidate symbols being denoted n B best symbols, with 1 ≤ n B < q, 1 ≤ n R < q and n R + n B < q. - n R measures of reliability obtained for n R candidate symbols selected by the non-binary variable node V j or by a first compression block implemented between the non-binary variable node V j and the non-binary constraint node C, said n R candidate symbols being denoted n R requested symbols, - n B measures of reliability obtained for n B candidate symbols selected by the non-binary constraint node C or by a second compression block implemented between the non-binary constraint node C and the non-binary variable node V j , said n B candidate symbols being denoted n B best symbols, with 1 ≤ n B < q, 1 ≤ n R < q and n R + n B < q. <EOS>