Bounds on the maximum-likelihood decoding error probability of low-density parity-check codes

We derive both upper and lower bounds on the decoding error probability of maximum-likelihood (ML) decoded low-density parity-check (LDPC) codes. The results hold for any binary-input symmetric-output channel. Our results indicate that for various appropriately chosen ensembles of LDPC codes, reliab...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 47; no. 7; pp. 2696 - 2710
Main Authors: Miller, G., Burshtein, D.
Format: Journal Article
Language:English
Published: IEEE 01.11.2001
Subjects:
Asymptotic properties
Channels
Decoding
Error detection coding
Errors
Exponents
Tightness
Upper bounds
ISSN:0018-9448
Online Access:Get full text
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Summary:We derive both upper and lower bounds on the decoding error probability of maximum-likelihood (ML) decoded low-density parity-check (LDPC) codes. The results hold for any binary-input symmetric-output channel. Our results indicate that for various appropriately chosen ensembles of LDPC codes, reliable communication is possible up to channel capacity. However, the ensemble averaged decoding error probability decreases polynomially, and not exponentially. The lower and upper bounds coincide asymptotically, thus showing the tightness of the bounds. However, for ensembles with suitably chosen parameters, the error probability of almost all codes is exponentially decreasing, with an error exponent that can be set arbitrarily close to the standard random coding exponent.
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ISSN:0018-9448
DOI:10.1109/18.959254