Title :
Weight Distributions of Regular Low-Density Parity-Check Codes Over Finite Fields
Author :
Yang, Shengtian ; Honold, Thomas ; Chen, Yan ; Zhang, Zhaoyang ; Qiu, Peiliang
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 :
approximation theory; parity check codes; statistical distributions; asymptotic approximation; asymptotic growth rate; average weight distribution; finite fields; regular LDPC code ensemble; regular low-density parity-check codes; Iterative decoding; Maximum likelihood estimation; Polynomials; Low-density parity-check (LDPC) codes; minimum distance; weight distribution;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2011.2162642
