Journal of VLSI Signal Processing Systems
Generic erasure correcting sets: bounds and constructions
Journal of Combinatorial Theory Series A - Special issue in honor of Jacobus H. van Lint
On the Stopping Distance and Stopping Redundancy of Finite Geometry LDPC Codes
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
On the Stopping Distance and Stopping Redundancy of Product Codes
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
A note on the stopping redundancy of linear codes
Journal of Computer Science and Technology
Good concatenated code ensembles for the binary erasure channel
IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
A cutting-plane method based on redundant rows for improving fractional distance
IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
Eliminating small stopping sets in irregular low-density parity-check codes
IEEE Communications Letters
Evaluation and design of irregular LDPC codes using ACE spectrum
IEEE Transactions on Communications
IEEE Transactions on Wireless Communications
The trapping redundancy of linear block codes
IEEE Transactions on Information Theory
Finding all small error-prone substructures in LDPC codes
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
On the stopping distance of array code parity-check matrices
IEEE Transactions on Information Theory
Single-exclusion number and the stopping redundancy of MDS codes
IEEE Transactions on Information Theory
An efficient algorithm to find all small-size stopping sets of low-density parity-check matrices
IEEE Transactions on Information Theory
On Linear Programming Decoding on a Quantized Additive White Gaussian Noise Channel
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Performance of polar codes for channel and source coding
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
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
Capacity-approaching irregular turbo codes for the binary erasure channel
IEEE Transactions on Communications
Multiple-bases belief-propagation decoding of high-density cyclic codes
IEEE Transactions on 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 | 755.20 |
It is now well known that the performance of a linear code Copf under iterative decoding on a binary erasure channel (and other channels) is determined by the size of the smallest stopping set in the Tanner graph for Copf. Several recent papers refer to this parameter as the stopping distance s of Copf. This is somewhat of a misnomer since the size of the smallest stopping set in the Tanner graph for Copf depends on the corresponding choice of a parity-check matrix. It is easy to see that s les d, where d is the minimum Hamming distance of Copf, and we show that it is always possible to choose a parity-check matrix for Copf (with sufficiently many dependent rows) such that s=d. We thus introduce a new parameter, the stopping redundancy of Copf, defined as the minimum number of rows in a parity- check matrix H for Copf such that the corresponding stopping distance s(H) attains its largest possible value, namely, s(H)=d. We then derive general bounds on the stopping redundancy of linear codes. We also examine several simple ways of constructing codes from other codes, and study the effect of these constructions on the stopping redundancy. Specifically, for the family of binary Reed-Muller codes (of all orders), we prove that their stopping redundancy is at most a constant times their conventional redundancy. We show that the stopping redundancies of the binary and ternary extended Golay codes are at most 34 and 22, respectively. Finally, we provide upper and lower bounds on the stopping redundancy of MDS codes