LDPC codes based on mutually orthogonal Latin rectangles and their application in perpendicular magnetic recording

We present a large family of low-density parity-check (LDPC) codes constructed from mutually orthogonal Latin rectangles. The construction is conceptually simple and gives high-rate LDPC codes with a structure of the parity check matrix that leads to a low complexity implementation of encoders and decoders. The bit-error rate characteristics are characterized by simulations of the soft iterative decoding in perpendicular magnetic read channels with different partial-response targets and types of noise.