Analysis of Absorbing Sets and Fully Absorbing Sets of Array-Based LDPC Codes
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Dolecek-2010-Analysis of Absorbing Sets and Fully Absorbing Sets of Array-Based LDPC Codes.pdf
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Author(s)
Dolecek, Lara
Zhang, Zhengya
Anantharam, Venkat
Wainwright, Martin J.
Nikolic, Borivoje
Date Issued
December 2009
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Dolecek, Lara et al. “Analysis of Absorbing Sets and Fully Absorbing Sets of Array-Based LDPC Codes.” IEEE Transactions on Information Theory 56.1 (2010): 181–201. © Copyright 2010 IEEE
Version
Final published version
Abstract
The class of low-density parity-check (LDPC) codes is attractive, since such codes can be decoded using practical message-passing algorithms, and their performance is known to approach the Shannon limits for suitably large block lengths. For the intermediate block lengths relevant in applications, however, many LDPC codes exhibit a so-called ¿error floor,¿ corresponding to a significant flattening in the curve that relates signal-to-noise ratio (SNR) to the bit-error rate (BER) level. Previous work has linked this behavior to combinatorial substructures within the Tanner graph associated with an LDPC code, known as (fully) absorbing sets. These fully absorbing sets correspond to a particular type of near-codewords or trapping sets that are stable under bit-flipping operations, and exert the dominant effect on the low BER behavior of structured LDPC codes. This paper provides a detailed theoretical analysis of these (fully) absorbing sets for the class of Cp, ¿ array-based LDPC codes, including the characterization of all minimal (fully) absorbing sets for the array-based LDPC codes for ¿ = 2,3,4, and moreover, it provides the development of techniques to enumerate them exactly. Theoretical results of this type provide a foundation for predicting and extrapolating the error floor behavior of LDPC codes.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1109/tit.2009.2034781
