The trapping redundancy of linear block codes

Authors:
Stefan Laendner;Thorsten Hehn;Olgica Milenkovic;Johannes B. Huber
Affiliations:
Institute for Information Transmission, University of Erlangen-Nuremberg, Erlangen, Germany;Institute for Information Transmission, University of Erlangen-Nuremberg, Erlangen, Germany;Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL;Institute for Information Transmission, University of Erlangen-Nuremberg, Erlangen, Germany
Venue:
IEEE Transactions on Information Theory
Year:
2009

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Abstract

We generalize the notion of the stopping redundancy in order to study the smallest size of a trapping set in Tanner graphs of linear block codes. In this context, we introduce the notion of the trapping redundancy of a code, which quantifies the relationship between the number of redundant rows in any parity-check matrix of a given code and the size of its smallest trapping set. Trapping sets with certain parameter sizes are known to cause error-floors in the performance curves of iterative belief propagation (BP) decoders, and it is therefore important to identify decoding matrices that avoid such sets. Bounds on the trapping redundancy are obtained using probabilistic and constructive methods, and the analysis covers both general and elementary trapping sets. Numerical values for these bounds are computed for the [2640,1320] Margulis code and the class of projective geometry codes, and compared with some new code-specific trapping set size estimates.