English

Weight Distributions of Regular Low-Density Parity-Check Codes over Finite Fields

Information Theory 2015-03-17 v3 math.IT

Abstract

The average weight distribution of a regular low-density parity-check (LDPC) code ensemble over a finite field is thoroughly analyzed. In particular, a precise asymptotic approximation of the average weight distribution is derived for the small-weight case, and a series of fundamental qualitative properties of the asymptotic growth rate of the average weight distribution are proved. Based on this analysis, a general result, including all previous results as special cases, is established for the minimum distance of individual codes in a regular LDPC code ensemble.

Keywords

Cite

@article{arxiv.1010.2030,
  title  = {Weight Distributions of Regular Low-Density Parity-Check Codes over Finite Fields},
  author = {Shengtian Yang and Thomas Honold and Yan Chen and Zhaoyang Zhang and Peiliang Qiu},
  journal= {arXiv preprint arXiv:1010.2030},
  year   = {2015}
}

Comments

15 pages, 5 figures, accepted for publication in IEEE Transactions on Information Theory, July 2011