Generalized Low-Density Parity-Check Codes Based on Hadamard Constraints

In this paper, we consider the design and analysis of generalized low-density parity-check (GLDPC) codes in AWGN channels. The GLDPC codes are specified by a bipartite Tanner graph, as with standard LDPC codes, but with the single parity-check constraints replaced by general coding constraints. In p...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 53; no. 3; pp. 1058 - 1079
Main Authors: Yue, Guosen, Ping, Li, Wang, Xiaodong
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.03.2007
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Applied sciences
AWGN channels
Code optimization
Code standards
Codes
Coding, codes
Communication channels
Convergence
Decoding
Density
Dynamical systems
Dynamics
Error correction
Error correction codes
Exact sciences and technology
extrinsic mutual information transfer (EXIT) chart
generalized low-density parity-check (GLDPC) codes
Graphs
Information theory
Information, signal and communications theory
Iterative algorithms
Iterative decoding
low-complexity decoding
low-density parity- check (LDPC)-Hadamard codes
low-rate
Mutual information
Noise levels
Optimization algorithms
Optimization methods
Parity check codes
Performance evaluation
Signal and communications theory
Simulation
Systems, networks and services of telecommunications
Telecommunications
Telecommunications and information theory
Transmission and modulation (techniques and equipments)
Performance evaluation
Block code
Iterative method
Dynamical system
Optimization
low-density parity- check (LDPC)-Hadamard codes
AWGN channels
extrinsic mutual information transfer (EXIT) chart
Coding
low-complexity decoding
Convergence rate
Parity check codes
Bipartite graph
Hadamard codes
generalized low-density parity-check (GLDPC) codes
Code optimization
Tanner graph
Turbo code
Decoding
low-rate
Algorithm
Information transmission
Message passing
Posterior probability
Simulation
Hadamard transformation
Error correcting code
Mutual information
Parity check
ISSN:0018-9448, 1557-9654
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Summary:In this paper, we consider the design and analysis of generalized low-density parity-check (GLDPC) codes in AWGN channels. The GLDPC codes are specified by a bipartite Tanner graph, as with standard LDPC codes, but with the single parity-check constraints replaced by general coding constraints. In particular, we consider imposing Hadamard code constraints at the check nodes for a low-rate approach, termed LDPC-Hadamard codes. We introduce a low-complexity message-passing based iterative soft-input soft-output (SISO) decoding algorithm, which employs the a posteriori probability (APP) fast Hadamard transform (FHT) for decoding the Hadamard check codes at each decoding iteration. The achievable capacity with the GLDPC codes is then discussed. A modified LDPC-Hadamard code graph is also proposed. We then optimize the LDPC-Hadamard code ensemble using a low-complexity optimization method based on approximating the density evolution by a one-dimensional dynamic system represented by an extrinsic mutual information transfer (EXIT) chart. Simulation results show that the optimized LDPC-Hadamard codes offer better performance in the low-rate region than low-rate turbo-Hadamard codes, but also enjoy a fast convergence rate. A rate-0.003 LDPC-Hadamard code with large block length can achieve a bit-error-rate (BER) performance of 10 -5 at -1.44 dB, which is only 0.15 dB away from the ultimate Shannon limit (-1.592 dB) and 0.24 dB better than the best performing low-rate turbo-Hadamard codes
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2006.890694