ORCID
- Ambroze, Adrian: 0000-0001-9021-1095
Abstract
In this work, we study the minimum/stopping distance of array low-density parity-check (LDPC) codes. An array LDPC code is a quasi-cyclic LDPC code specified by two integers q and m, where q is an odd prime and m <= q. In the literature, the minimum/stopping distance of these codes (denoted by d(q,m) and h(q,m), resp.) has been thoroughly studied for m <= 5. Both exact results, for small values of q and m, and general (i.e., independent of q) bounds have been established. For m=6, the best known minimum distance upper bound, derived by Mittelholzer (IEEE Int. Symp. Inf. Theory, Jun./Jul. 2002), is d(q,6) <= 32. In this work, we derive an improved upper bound of d(q,6) <= 20 and a new upper bound d(q,7) <= 24 by using a new concept of a template support matrix of a codeword/stopping set. The bounds are tight with high probability in the sense that we have not been able to find codewords of strictly lower weight for several values of q using a minimum distance probabilistic algorithm. Finally, we provide new specific minimum/stopping distance results for m <= 7 and low-to-moderate values of q <= 79.
DOI
10.1109/TIT.2014.2333519
Publication Date
2014-07-11
Publication Title
IEEE Transactions on Information Theory
Volume
60
Issue
9
ISSN
0018-9448
Organisational Unit
School of Engineering, Computing and Mathematics
First Page
5204
Last Page
5214
Recommended Citation
Rosnes, E., Ambroze, M., & Tomlinson, M. (2014) 'On the Minimum/Stopping Distance of Array Low-Density Parity-Check Codes', IEEE Transactions on Information Theory, 60(9), pp. 5204-5214. Available at: https://doi.org/10.1109/TIT.2014.2333519
