Shaping methods for low-density lattice codes

Abstract

Low density lattice codes (LDLC) are recently-proposed 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 <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. In order to design practical lattice codes, the infinite lattice should be combined with a shaping algorithm, that maps information bits to lattice points and ensures that the power of the lattice codewords is properly constrained. This work proposes several efficient and practical shaping algorithms for LDLC.