Iterative decoder configured for decoding a codeword of a code represented by a Tanner graph and having a codeword length N, said iterative decoder comprising: • N variable nodes (VNs) v n, n = 1... N, each variable node v n being configured to receive a log-likelihood ratio LLR I n of a channel decoded bit n of the codeword to be decoded, said LLR I n being defined on an alphabet A L of q ch quantization bits, q ch being an integer equal or greater than 2; • M constraint nodes (CNs) c m, m = 1... M, 2 ≤ M < N; • the variable nodes and the constraint nodes representing nodes of the Tanner graph where the variable nodes and the constraint nodes are configured to exchange messages along edges of the Tanner graph; • each variable node v n being configured for estimating an a posteriori probability, APP, value of the n th bit of the codeword to be decoded and for sending messages m v n →c m belonging to an alphabet A s of q quantization bits, q ≤ q ch, to the connected constraint nodes c m, where a set of connected constraint nodes is denoted V (vn), a degree d v of the variable node v n is defined as the size of the set V (vn), and the set V (vn) except the constraint node c m is denoted V (vn)\{cm}, • each constraint nodes c m being configured for testing the received message with predetermined constraints and sending messages m c m →v n, messages belonging to an alphabet A c of q' quantization bits, having a different or similar set of value than A s, to the connected variable nodes v n; • the message emissions being repeated until the decoding of the codeword is achieved successfully or a predetermined number of iterations is reached; characterized in that • the LLR I n and the messages m v n → c m and m c m → v n are coded according to a sign-and-magnitude code in the alphabets A L, A s and A c symmetric around zero, A L = {-N qch,..., -1, -0, +0, +1,...,+N qch}, A s = {-N q,..., -1, -0, +0, +1,...,+N q}, A c = {-N q',..., -1, -0, +0, +1,...,+N q'} in which the sign indicates the estimated bit value and the magnitude represents its reliability; and • each variable node v n, for each iteration l, is configured to compute: • sign-preserving factors, for each connected constraint node c m as a sum of a ponderated sign of the LLR I n and a sum of the signs of all messages, except for the message coming from c m, received from the connected constraint nodes at iteration l: μ v n → c m l = ξ × sign I n + ∑ c ∈ V v n ∖ c m sign m c → v n l where ξ is a positive or a null integer, and • messages to connected constraint nodes c m for iteration l +1 in two steps: m v n → c m l + 1, U = I n + 1 2 × μ v n → c m l + ∑ c ∈ V v n ∖ c m m c → v n l and where S is a function from the set of values that can take floor abs m v n → c m l + 1, U to the alphabet A s. • N variable nodes (VNs) v n, n = 1... N, each variable node v n being configured to receive a log-likelihood ratio LLR I n of a channel decoded bit n of the codeword to be decoded, said LLR I n being defined on an alphabet A L of q ch quantization bits, q ch being an integer equal or greater than 2; • M constraint nodes (CNs) c m, m = 1... M, 2 ≤ M < N; • the variable nodes and the constraint nodes representing nodes of the Tanner graph where the variable nodes and the constraint nodes are configured to exchange messages along edges of the Tanner graph; • each variable node v n being configured for estimating an a posteriori probability, APP, value of the n th bit of the codeword to be decoded and for sending messages m v n →c m belonging to an alphabet A s of q quantization bits, q ≤ q ch, to the connected constraint nodes c m, where a set of connected constraint nodes is denoted V (vn), a degree d v of the variable node v n is defined as the size of the set V (vn), and the set V (vn) except the constraint node c m is denoted V (vn)\{cm}, • each constraint nodes c m being configured for testing the received message with predetermined constraints and sending messages m c m →v n, messages belonging to an alphabet A c of q' quantization bits, having a different or similar set of value than A s, to the connected variable nodes v n; • the message emissions being repeated until the decoding of the codeword is achieved successfully or a predetermined number of iterations is reached; characterized in that • the LLR I n and the messages m v n → c m and m c m → v n are coded according to a sign-and-magnitude code in the alphabets A L, A s and A c symmetric around zero, A L = {-N qch,..., -1, -0, +0, +1,...,+N qch}, A s = {-N q,..., -1, -0, +0, +1,...,+N q}, A c = {-N q',..., -1, -0, +0, +1,...,+N q'} in which the sign indicates the estimated bit value and the magnitude represents its reliability; and • each variable node v n, for each iteration l, is configured to compute: • sign-preserving factors, for each connected constraint node c m as a sum of a ponderated sign of the LLR I n and a sum of the signs of all messages, except for the message coming from c m, received from the connected constraint nodes at iteration l: μ v n → c m l = ξ × sign I n + ∑ c ∈ V v n ∖ c m sign m c → v n l where ξ is a positive or a null integer, and • messages to connected constraint nodes c m for iteration l +1 in two steps: m v n → c m l + 1, U = I n + 1 2 × μ v n → c m l + ∑ c ∈ V v n ∖ c m m c → v n l and where S is a function from the set of values that can take floor abs m v n → c m l + 1, U to the alphabet A s.