Low density parity check lattices

Mohammad Ali Sadeghi, Daniel Panario

Mohammad‐Reza Sadeghi, Daniel Panario

李铁楠, 单秀玲

Mohammad‐Reza Sadeghi, Amir H. Banihashemi, Daniel Panario

Low-density parity-check codes (LDPC) can have an impressive performance under iterative decoding algorithms. In this paper we introduce a method to construct high coding gain lattices with low decoding complexity based on LDPC codes. To construct such lattices we apply Construction D', due to Bos, Conway, and Sloane, to a set of parity checks defining a family of nested LDPC codes. For the decoding algorithm, we generalize the application of max-sum algorithm to the Tanner graph of lattices. Bounds on the decoding complexity are derived and our analysis shows that using LDPC codes results in low decoding complexity for the proposed lattices. The progressive edge growth (PEG) algorithm is then extended to construct a class of nested regular LDPC codes which are in turn used to generate low density parity check lattices. Using this approach, a class of two-level lattices is constructed. The performance of this class improves when the dimension increases and is within 3 dB of the Shannon limit for error probabilities of about 10-6. This is while the decoding complexity is still quite manageable even for dimensions of a few thousands

Marco Baldi

Young-Seob Choi, Ihn-Jung Baik, Sae-Young Chung

Low-density parity-check (LDPC) lattices are introduced by Sadeghi et al. (2006). The construction method of such lattices and the decoding algorithm based on the min-sum algorithm are also proposed in [1]. In this paper we apply two iterative message passing algorithms, the sum-product algorithm and the max-product algorithm, to the Tanner graph representation of LDPC lattices. We evaluate the performance of two iterative message passing algorithms.