NDLI: Low-Density Parity-Check Lattices: Construction and Decoding Analysis

Content Provider	IEEE Xplore Digital Library
Author	Sadeghi, M.-R. Banihashemi, A.H. Panario, D.
Copyright Year	1963
Abstract	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
Sponsorship	IEEE Information Theory Society
Starting Page	4481
Ending Page	4495
Page Count	15
File Size	986990
File Format	PDF
ISSN	00189448
Volume Number	52
Issue Number	10
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-10-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Parity check codes Lattices Iterative decoding AWGN Iterative algorithms Error probability Gaussian noise Signal to noise ratio Broadband communication Wireless communication Tanner graphs Additive white Gaussian noise (AWGN) channel iterative decoding lattice codes lattices low-density parity-check (LDPC) codes low-density parity-check (LDPC) lattices min-sum algorithm progressive-edge growth (PEG) construction
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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