2007/04/11 by Naftali Sommer, Meir Feder, Sommer, Naftali +3
Computer Science · Mathematics · #Cellular Automata and Applications #Coding theory and cryptography #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.0704.1317
24 pages, 4 figures. Submitted for publication in IEEE transactions on Information Theory
arxiv created 2007/04/11 · openalex publication_date 2007/04/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.