Low Density Lattice Codes

Details Low Density Lattice Codes Low Density Lattice Codes

2007-04-11

arxiv.org/abs/0704.1317v1

Computer Science

Information Theory

24 pages, 4 figures. Submitted for publication in IEEE transactions on Information Theory

Scientific paper

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, the inverse of G, 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 ~0.5dB from capacity at block length of n = 100,000 symbols. The paper also discusses convergence results and implementation considerations.

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