Low Density Lattice Codes

Abstract

Low density lattice codes (LDLC) are novel lattice codes that can approach the capacity of the additive white Gaussian noise (AWGN) channel and be decoded efficiently. 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 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> 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