Capacity Achieving LDPC Codes Through Puncturing

The performance of punctured low-definition parity-check (LDPC) codes under maximum-likelihood (ML) decoding is studied in this correspondence via deriving and analyzing their average weight distributions (AWDs) and the corresponding asymptotic growth rate of the AWDs. In particular, it is proved th...

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Bibliographic Details
Published in:IEEE transactions on information theory 2008-10, Vol.54 (10), p.4698-4706
Main Authors: Chun-Hao Hsu, Anastasopoulos, A.
Format: Article
Language:English
Subjects:
Applied sciences
Asymptotic growth rate
Asymptotic properties
average weight distribution
AWGN
capacity-achieving codes
Channels
Codes
Coding
Coding, codes
Concatenated codes
Construction
Data processing
Decoding
Exact sciences and technology
Graph theory
H infinity control
Information theory
Information, signal and communications theory
Input output
Iterative decoding
low-density parity-check (LDPC) codes
Maximum likelihood decoding
Maximum likelihood method
maximum-likelihood (ML) decoding
Mobile communication
Parity check codes
Performance analysis
Piercing
punctured codes
rate-adaptable codes
Signal and communications theory
Studies
Telecommunications and information theory
Wireless networks
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Summary:The performance of punctured low-definition parity-check (LDPC) codes under maximum-likelihood (ML) decoding is studied in this correspondence via deriving and analyzing their average weight distributions (AWDs) and the corresponding asymptotic growth rate of the AWDs. In particular, it is proved that capacity-achieving codes of any rate and for any memoryless binary-input output-symmetric (MBIOS) channel under ML decoding can be constructed by puncturing some original LDPC code with small enough rate. Moreover, it is shown that the gap to capacity of all the punctured codes can be the same as the original code with a small enough rate. Conditions under which puncturing results in no rate loss with asymptotically high probability are also given in the process. These results show high potential for puncturing to be used in designing capacity-achieving codes, and in rate-compatible coding under any MBIOS channel.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2008.928274