2016/03/22 by Hassan Khodaiemehr, Khodaiemehr, Hassan, Mohammad‐Reza Sadeghi +4
Computer Science · Engineering · Mathematics · #Advanced Wireless Communication Techniques #Cooperative Communication and Network Coding #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1603.07010
Submitted for possible publication
arxiv created 2016/03/22 · openalex publication_date 2016/03/22 · arxiv updated 2016/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
LDPC lattices were the first family of lattices that equipped with iterative decoding algorithms under which they perform very well in high dimensions. In this paper, we introduce quasi cyclic low density parity check (QC-LDPC) lattices as a special case of LDPC lattices with one binary QC-LDPC code as their underlying code. These lattices are obtained from Construction A of lattices providing us to encode them efficiently using shift registers. To benefit from an encoder with linear complexity in dimension of the lattice, we obtain the generator matrix of these lattices in "quasi cyclic" form. We provide a low-complexity decoding algorithm of QC-LDPC lattices based on sum product algorithm. To design lattice codes, QC-LDPC lattices are combined with nested lattice shaping that uses the Voronoi region of a sublattice for code shaping. The shaping gain and shaping loss of our lattice codes with dimensions 40, 50 and 60 using an optimal quantizer, are presented. Consequently, we establish a family of lattice codes that perform practically close to the sphere bound.