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Low density lattice codes (LDLC) are novel lattice codes that can be decoded efficiently and approach the capacity of the additive white Gaussian noise (AWGN) channel. In LDLC a codeword x is generated directly at the n-dimensional Euclidean space as a linear transformation of a corresponding integer message vector b, i.e., x = Gb, where H = G −1 is restricted to be sparse. The fact that H is sparse is utilized to develop a lineartime iterative decoding scheme which attains, as demonstrated bydoi:10.1109/isit.2006.261680 dblp:conf/isit/SommerFS06 fatcat:fh3hjjublzcfddtxoro6fowk6q