On the performance of 1-level LDPC lattices

The low-density parity-check (LDPC) lattices perform very well in high dimensions under generalized min-sum iterative decoding algorithm. In this work we focus on 1-level LDPC lattices. We show that these lattices are the same as lattices constructed based on Construction A and low-density lattice-code (LDLC) lattices. In spite of having slightly lower coding gain, 1-level regular LDPC lattices have remarkable performances. The lower complexity nature of the decoding algorithm for these type of lattices allows us to run it for higher dimensions easily. Our simulation results show that a 1-level LDPC lattice of size 10000 can work as close as 1.1 dB at normalized error probability (NEP) of $10^{-5}$.This can also be reported as 0.6 dB at symbol error rate (SER) of $10^{-5}$ with sum-product algorithm.Comment: 1 figure, submitted to IWCIT 201

Low Density Lattice Codes

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 on Information Theor