The Trapping Redundancy of Linear Block Codes
arXiv:cs/0701006 · doi:10.1109/TIT.2008.2008134
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 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.
12 pages, 4 tables, 1 figure, accepted for publication in IEEE Transactions on Information Theory
References in corpus (3)
Cited by in corpus (8)
- Bounds on Separating Redundancy of Linear Codes and Rates of X-Codes
- An Efficient Algorithm for Finding Dominant Trapping Sets of LDPC Codes
- New Characterization and Efficient Exhaustive Search Algorithm for Elementary Trapping Sets of Variable-Regular LDPC Codes
- Error Floor Approximation for LDPC Codes in the AWGN Channel
- Probabilistic bounds on the trapping redundancy of linear codes
- LDPC Code Density Evolution in the Error Floor Region
- On Characterization of Elementary Trapping Sets of Variable-Regular LDPC Codes
- Characterization and Efficient Exhaustive Search Algorithm for Elementary Trapping Sets of Irregular LDPC Codes