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.Comment: 24 pages, 4 figures. Submitted for publication in IEEE transactions
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