Low complexity construction of low density lattice codes based on array codes

Recently a variety of lattices called low density lattices codes (LDLC) have been studied because they can be decoded efficiently using belief propagation, and can be seen as a Euclidean space codes analogue to low density parity check codes (LDPC). Previous LDLC lattice designs, like Latin square, are based on high-complexity computer search to eliminate 4-cycles. Array codes have been used to construct LDPC codes efficiently. This work describes the design of LDLC based on array codes. This construction is 4-cycle free and a systematic construction of the parity check matrix. For all cases considered, the LDLC based on array codes have a better symbol error rate performance than the latin square. For example, there is a 0.5 dB gain for dimension n = 91.