US Patent 7168033 Parity check matrix and method of forming thereof

A decoder for decoding data from a communication channel includes a parity check matrix including M tiers, wherein M≧B, Dmin=B*M for M=1 . . . E or B*M≧Dmin≧F for M>E. Dmin is the minimum Hamming distance and tc=M, wherein tc is a column weight. The parity check matrix includes no period-four cycles. B, Dmin, E, F and M are integers. A soft channel decoder is configured to decode data. A soft linear block code decoder is configured to decode data decoded by the soft channel decoder in accordance with the parity check matrix.