Low-Density Lattice Codes

摘要

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 $underline {x}$ is generated directly at the $n$-dimensional Euclidean space as a linear transformation of a corresponding integer message vector $underline {b}$ , i.e., $underline {x}= mmb {G}underline {b}$, where $ mmb {H}= mmb {G}^{-1}$ is restricted to be sparse. The fact that $ mmb {H}$ is sparse is utilized to develop a linear-time iterative decoding scheme which attains, as demonstrated by simulations, good error performance within $sim $0.5 dB from capacity at block length of $n=$100,000 symbols. The paper also discusses convergence results and implementation considerations.