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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Vydáno v:	IEEE transactions on information theory Ročník 53; číslo 3; s. 1058 - 1079
Hlavní autoři:	Yue, Guosen, Ping, Li, Wang, Xiaodong
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.03.2007 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	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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Shrnutí:	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
Bibliografie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2006.890694