On the Stopping Distance and Stopping Redundancy of Product Codes
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
A Combined Matrix Ensemble of Low-Density Parity-Check Codes for Correcting a Solid Burst Erasure
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Instanton-based techniques for analysis and reduction of error floors of LDPC codes
IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
Capacity-approaching protograph codes
IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
Finding all small error-prone substructures in LDPC codes
IEEE Transactions on Information Theory
Upper bound on error exponent of regular LDPC codes transmitted over the BEC
IEEE Transactions on Information Theory
On the stopping distance of array code parity-check matrices
IEEE Transactions on Information Theory
Weight distributions of multi-edge type LDPC codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
On the probabilistic computation of the stopping redundancy of LDPC codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Finite-length rate-compatible LDPC codes: a novel puncturing scheme
IEEE Transactions on Communications
Design of irregular LDPC codes with optimized performance-complexity tradeoff
IEEE Transactions on Communications
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Analysis of absorbing sets and fully absorbing sets of array-based LDPC codes
IEEE Transactions on Information Theory
Protograph LDPC codes over burst erasure channels
MILCOM'06 Proceedings of the 2006 IEEE conference on Military communications
Hardness of approximation results for the problem of finding the stopping distance in tanner graphs
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Stopping set distributions of algebraic geometry codes from elliptic curves
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
| Hi-index | 755.08 |
Stopping sets determine the performance of low-density parity-check (LDPC) codes under iterative decoding over erasure channels. We derive several results on the asymptotic behavior of stopping sets in Tanner-graph ensembles, including the following. An expression for the normalized average stopping set distribution, yielding, in particular, a critical fraction of the block length above which codes have exponentially many stopping sets of that size. A relation between the degree distribution and the likely size of the smallest nonempty stopping set, showing that for a √1-λ'(0)ρ'(1) fraction of codes with λ'(0)ρ'(1)2, the smallest nonempty stopping set is linear in the block length. Bounds on the average block error probability as a function of the erasure probability ε, showing in particular that for codes with lowest variable degree 2, if ε is below a certain threshold, the asymptotic average block error probability is 1-√1-λ'(0)ρ'(1)ε.