Tight Bounds of minimum Distance Distributions of Irregular LDPC Code Ensembles

健太 笠井, Kenta Kasai

Tomoharu Shibuya

Shinya Miyamoto, Kenta Kasai, Tomoharu Shibuya +1 more

Upper bounds of minimum distance distributions of Gallger codes and irregular LDPC codes were derived by Callage and Di, respectively. Di's bounds are tight for irregular LDPC codes which have variable nodes of degree two, however, it is not tight for irregular LDPC codes which do not. In this paper, we derive tight lower and upper bounds of minimum distance distributions of irregular LDPC code ensembles without variable nodes of degree two.

Ian P. Mulholland, Mark F. Flanagan, Enrico Paolini

In this paper, the minimum distance distribution of irregular generalized LDPC (GLDPC) code ensembles is investigated. Two classes of GLDPC code ensembles are analyzed; in one case, the Tanner graph is regular from the variable node perspective, and in the other case the Tanner graph is completely unstructured and irregular. In particular, for the former ensemble class we determine exactly which ensembles have minimum distance growing linearly with the block length with probability approaching unity with increasing block length. This work extends previous results concerning LDPC and regular GLDPC codes to the case where a hybrid mixture of check node types is used.

亮志 池谷

D. Divsalar

Recently, LDPC codes with projected graph, or protograph structures have been proposed. In this paper, finite length ensemble weight enumerators for LDPC codes with protograph structures are obtained. Asymptotic results are derived as the block size goes to infinity. In particular, we are interested in obtaining ensemble average weight enumerators for protograph LDPC codes which have typical minimum distance that grows linearly with block size. As with irregular ensembles, linear minimum distance property is sensitive to the proportion of degree-2 variable nodes. In this paper, the derived results on ensemble weight enumerators show that linear minimum distance condition on degree distribution of unstructured irregular LDPC codes is a sufficient but not a necessary condition for protograph LDPC codes