Encoding of a low-density parity check code uses a block-circulant encoding matrix built from circulant matrices. Encoding can include partitioning data into a plurality of data segments. The data segments are each circularly rotated. A plurality of XOR summations are formed for each rotation of the data segments to produce output symbols. The XOR summations use data from the data segments defined by the circulant matrices. Output symbols are produced in parallel for each rotation of the data segments.