@article{08b2cebdb50d4b438725fa0c78888c54,
title = "Distance Distributions in Ensembles of Irregular Low-Density Parity-Check Codes",
abstract = "The estimation of the average distance distribution in ensembles of irregular low-density parity-check (LDPC) codes was discussed using asymptotic expressions. The derivation defined the considered ensemble of irregular codes and the average distance distribution. The number of matrices belonging to the ensemble of special shape were counted. The defined codes contained the word with on the first ω positions and zero on the remaining positions. A discussion on the number of solutions to a system of equation appearing in the optimization problem was also presented.",
keywords = "Distance distributions, Low-density parity-check (LDPC) codes",
author = "Simon Litsyn and Vladimir Shevelev",
note = "Funding Information: Manuscript received July 31, 2001; revised July 30, 2003. This work was supported by the Israeli Science Foundation under Grant 0511-00. The work of V. Shevelev is supported in part by the Israeli Ministry of Absorption. S. Litsyn is with the Department of Electrical Engineering–Systems, Tel-Aviv University, Ramat-Aviv 69978, Israel (e-mail:litsyn@eng.tau.ac.il). V. Shevelev is with the Department of Mathematics, Ben Gurion University, Beer-Sheva 84105, Israel (e-mail: shevelev@bgumail.bgu.ac.il). Communicated by R. Urbanke, Associate Editor for Coding Techniques. Digital Object Identifier 10.1109/TIT.2003.820012",
year = "2003",
month = dec,
doi = "10.1109/TIT.2003.820012",
language = "אנגלית",
volume = "49",
pages = "3140--3159+3353",
journal = "IEEE Transactions on Information Theory",
issn = "0018-9448",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "12",
}