Trapping and Absorbing Set Enumerators for Irregular Generalized Low-Density Parity-Check Code Ensembles

The definitions of (elementary) trapping and (fully) absorbing sets are extended to generalized low-density parity-check (GLDPC) codes. In particular, the fully absorbing sets are stable under the bit flipping algorithm. The finite-length (elementary) trapping and (fully) absorbing set enumerators f...

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Bibliographic Details
Published in:IEEE transactions on information theory 2023-06, Vol.69 (6), p.1-1
Main Author: Yacoub, Emna Ben
Format: Article
Language:English
Subjects:
absorbing sets
Algorithms
asymptotic enumeration
Asymptotic methods
Asymptotic properties
bit flipping
Block codes
Codes
Decoders
Decoding
Error correcting codes
irregular generalized LDPC codes
Iterative decoding
non-binary LDPC
Parity
Parity check codes
Simulation
Stability analysis
Trapping
Trapping sets
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Summary:The definitions of (elementary) trapping and (fully) absorbing sets are extended to generalized low-density parity-check (GLDPC) codes. In particular, the fully absorbing sets are stable under the bit flipping algorithm. The finite-length (elementary) trapping and (fully) absorbing set enumerators for unstructured irregular GLDPC code ensembles are derived using generating functions. An efficient method to evaluate the asymptotic trapping and (fully) absorbing set distributions is presented, which requires solving a system of equations. Using this method, the asymptotic distribution of trapping and (fully) absorbing sets are evaluated for some example GLDPC code ensembles. Experimental results show that the proposed definitions yield graph structures that are harmful for bit flipping decoders. The generating function approach is also used to derive the finite-length and asymptotic trapping and (elementary) absorbing set enumerators for non-binary irregular LDPC code ensembles.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2023.3240843