Low-density lattice codes

Low-density lattice codes (LDLQ 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) under bar, i.e., (x) under bar = G (b) under bar, where H = G(-1) is restricted to be sparse. The fact that H is sparse is utilized to develop a linear-time iterative decoding scheme which attains, as demonstrated by simulations, good error performance within -0.5 dB from capacity at block length of n. =100,000 symbols. The paper also discusses convergence results and implementation considerations.