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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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 47; no. 2; pp. 638 - 656
Main Authors: Richardson, T.J., Urbanke, R.L.
Format: Journal Article
Language:English
Published: New York IEEE 01.02.2001
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Binary system
Blocking
Codes
Complexity
Decoding
Encoders
Encoding
Error detection coding
Graphs
Mathematical analysis
Matrices
Matrix
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary: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.
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ISSN:0018-9448
1557-9654
DOI:10.1109/18.910579