Efficient encoding of low-density parity-check codes

Low-density parity-check (LDPC) codes can be considered serious competitors to turbo codes in terms of performance and complexity and they are based on a similar philosophy: constrained random code ensembles and iterative decoding algorithms. We consider the encoding problem for LDPC codes. More gen...

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Veröffentlicht in:	IEEE transactions on information theory Jg. 47; H. 2; S. 638 - 656
Hauptverfasser:	Richardson, T.J., Urbanke, R.L.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York IEEE 01.02.2001 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Algorithms Binary system Blocking Codes Complexity Decoding Encoders Encoding Error detection coding Graphs Mathematical analysis Matrices Matrix
ISSN:	0018-9448, 1557-9654
Online-Zugang:	Volltext
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Abstract	Low-density parity-check (LDPC) codes can be considered serious competitors to turbo codes in terms of performance and complexity and they are based on a similar philosophy: constrained random code ensembles and iterative decoding algorithms. We consider the encoding problem for LDPC codes. More generally we consider the encoding problem for codes specified by sparse parity-check matrices. We show how to exploit the sparseness of the parity-check matrix to obtain efficient encoders. For the (3,6)-regular LDPC code, for example, the complexity of encoding is essentially quadratic in the block length. However, we show that the associated coefficient can be made quite small, so that encoding codes even of length n/spl sime/100000 is still quite practical. More importantly, we show that "optimized" codes actually admit linear time encoding.
AbstractList	Low-density parity-check (LDPC) codes can be considered serious competitors to turbo codes in terms of performance and complexity and they are based on a similar philosophy: constrained random code ensembles and iterative decoding algorithms. We consider the encoding problem for LDPC codes. More generally we consider the encoding problem for codes specified by sparse parity-check matrices. We show how to exploit the sparseness of the parity-check matrix to obtain efficient encoders. For the (3,6)-regular LDPC code, for example, the complexity of encoding is essentially quadratic in the block length. However, we show that the associated coefficient can be made quite small, so that encoding codes even of length n/spl sime/100000 is still quite practical. More importantly, we show that "optimized" codes actually admit linear time encoding. Low-density parity-check (LDPC) codes can be considered serious competitors to turbo codes in terms of performance and complexity and they are based on a similar philosophy: constrained random code ensembles and iterative decoding algorithms. We consider the encoding problem for LDPC codes. More generally we consider the encoding problem for codes specified by sparse parity-check matrices. We show how to exploit the sparseness of the parity-check matrix to obtain efficient encoders. For the (3,6)-regular LDPC code, for example, the complexity of encoding is essentially quadratic in the block length. However, we show that the associated coefficient can be made quite small, so that encoding codes even of length n 100000 is still quite practical. More importantly, we show that "optimized" codes actually admit linear time encoding Low-density parity-check (LDPC) codes can be considered serious competitors to turbo codes in terms of performance and complexity and they are based on a similar philosophy: constrained random code ensembles and iterative decoding algorithms. We consider the encoding problem for LDPC codes. More generally we consider the encoding problem for codes specified by sparse parity-check matrices. We show how to exploit the sparseness of the parity-check matrix to obtain efficient encoders. For the (3,6)-regular LDPC code, for example, the complexity of encoding is essentially quadratic in the block length. However, we show that the associated coefficient can be made quite small, so that encoding codes even of length n[sime]100000 is still quite practical. More importantly, we show that "optimized" codes actually admit linear time encoding Low-density parity-check (LDPC) codes can he considered serious competitors to turbo codes in terms of performance and complexity and they are based on a similar philosophy constrained random code ensembles and iterative decoding algorithms.
Author	Urbanke, R.L. Richardson, T.J.
Author_xml	– sequence: 1 givenname: T.J. surname: Richardson fullname: Richardson, T.J. organization: Lucent Technol. Bell Labs., Murray Hill, NJ, USA – sequence: 2 givenname: R.L. surname: Urbanke fullname: Urbanke, R.L.
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References	ref13 ref12 ref15 ref14 Gallager (ref1) 1963 ref11 ref10 Luby (ref16) Zyablov (ref2) 1975; 11 Schrijver (ref19) 1986 ref17 ref18 ref8 ref7 ref9 ref4 ref3 ref6 ref5
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Snippet	Low-density parity-check (LDPC) codes can be considered serious competitors to turbo codes in terms of performance and complexity and they are based on a... Low-density parity-check (LDPC) codes can he considered serious competitors to turbo codes in terms of performance and complexity and they are based on a...
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StartPage	638
SubjectTerms	Algorithms Binary system Blocking Codes Complexity Decoding Encoders Encoding Error detection coding Graphs Mathematical analysis Matrices Matrix
Title	Efficient encoding of low-density parity-check codes
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