The codewords in bits may be decoded with the H_n, for example, using the message passing algorithm (MPA) with the LLR values. As illustrated in the example of FIG. 17, the LDPC decoding with MPA is an iterative decoding algorithm that uses the structure of the Tanner graph, which is the graphical representation of the LPDC parity check matrix H_n. In the LDPC decoder 1508, each check node 1702 determines the value of an erased bit based on the LLR value if it is the only erased bit in its parity-check equation. The messages passed along the Tanner graph edges 1706. For each iteration of the algorithm, each variable node 1704 sends a message (“extrinsic information”) to each check node 1702 to which the variable node 1704 is connected. Each check node 1702 sends a message (“extrinsic information”) to variable nodes 1704 to which the check node 1702 is connected. “Extrinsic” in this context means that the information the check nodes 1702 or variable nodes 1704 already possess is not passed to that node. A posteriori probability for each codeword bit is calculated based on the received signal at the LLR calculator 1506 and the parity constraints defined in the H_n, namely, to be a valid codeword c=[c₁, . . . , c_n], the Hc^T=0.

In decoding, as at least one submatrix in H_n comprises m₁ diagonals of “1”, where m₁>=2, the presence of superimposed layers in the parity-check matrix H_n has a minor impact in the implementation of the LDPC decoder 1508, which may be assumed to have a layered architecture.