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

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...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 52; no. 10; pp. 4481 - 4495
Main Authors: Sadeghi, M.-R., Banihashemi, A.H., Panario, D.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.10.2006
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Additive white Gaussian noise (AWGN) channel
Algorithms
Applied sciences
AWGN
Broadband communication
Codes
Coding, codes
Communications networks
Complexity
Construction
Decoding
Density
Error probability
Exact sciences and technology
Gaussian noise
Information, signal and communications theory
Iterative algorithms
Iterative decoding
lattice codes
Lattices
low-density parity-check (LDPC) codes
low-density parity-check (LDPC) lattices
Methods
min-sum algorithm
Noise levels
Parity
Parity check codes
progressive-edge growth (PEG) construction
Signal and communications theory
Signal to noise ratio
Tanner graphs
Telecommunications and information theory
Wireless communication
Performance evaluation
lattice codes
Error probability
low-density parity-check (LDPC) lattices
Additive white Gaussian noise (AWGN) channel
min-sum algorithm
Trellis code
Algorithm
Iterative decoding
Tanner graphs
low-density parity-check (LDPC) codes
progressive-edge growth (PEG) construction
Algorithm complexity
Parity check codes
Error correcting code
lattices
Parity check
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary: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
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2006.881720