Low Density Lattice Codes

Naftali Sommer; Meir Feder; Ofir Shalvi

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arXiv · 0704.1317

Low Density Lattice Codes

Naftali Sommer·Meir Feder·Ofir Shalvi

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Abstract

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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Naftali Sommer, Meir Feder, Ofir Shalvi. 2007-04-11. Low Density Lattice Codes. https://arxiv.org/abs/0704.1317

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