IEEE Transactions on Information Theory

Weight Distributions of Non-Binary Multi-Edge Type LDPC Code Ensembles: Analysis and Efficient Evaluation

Giuliano Garrammone, David Declercq, M.P.C. Fossorier

Published Jan 4, 2017• 7 citations

Abstract

Non-binary multi-edge type ensembles of low-density parity-check codes are analyzed in terms of non-binary codeword weight distribution and its growth rate. In particular, an exact expression of the growth rate for small weights is developed. As a side result, the stopping set distributions of these ensembles are developed. Examples of weight distributions are provided, showing that the derived closed-form expressions can be easily evaluated. The obtained results can thus be exploited to analyze and design non-binary low-density parity-check codes that fall within the multi-edge type framework such as, but not limited to, protograph-based codes.

DOI: 10.1109/tit.2016.2647724

Related papers

Weight distributions of non-binary multi-edge type LDPC code ensembles

Giuliano Garrammone, David Declercq, M.P.C. Fossorier

The non-binary codeword weight distribution and its growth rate are developed for non-binary multi-edge type ensembles of low-density parity-check codes. Moreover, an analysis of the growth rate for small weights is provided. The derived expressions can serve as powerful and flexible tools to analyze and design the non-binary low-density parity-check codes that fall within the multi-edge type framework.

IEEE International Symposium on Information Theory (ISIT)Jun 1, 20152 citations

Weight distribution of non-binary LDPC codes

Kenta Kasai, Charly Poulliat, David Declercq +2 more

Weight distributions of binary low-density parity-check (LDPC) codes are well studied. We investigate the average distributions of symbol and binary weight for non-binary LDPC code ensemble. We derive the asymptotic growth rate and its linear approximation for small weight. Moreover, we show the typical minimum distance does not monotonically increase with the size of the field where the codes are defined.

International Symposium on Information Theory and its ApplicationsDec 1, 200817 citations

Weight distribution for non-binary cluster LDPC code ensemble

隆之野﨑, Masaki Maehara, Kenta Kasai +1 more

This paper derives the average symbol and bit weight distributions for the irregular non-binary cluster low-density parity-check (LDPC) code ensembles.Moreover, we give the exponential growth rates of the average weight distributions in the limit of large code length.We show the condition that the typical minimum distances linearly grow with the code length.

Jul 1, 20130 citations

Weight distribution for non-binary cluster LDPC code ensemble

T. Nozaki, Masaki Maehara, Kenta Kasai +1 more

In this paper, we derive the average weight distributions for the irregular non-binary cluster low-density parity-check (LDPC) code ensembles. Moreover, we give the exponential growth rate of the average weight distribution in the limit of large code length. We show that there exist (2, dc)-regular non-binary cluster LDPC code ensembles whose normalized typical minimum distances are strictly positive.

IEEE International Symposium on Information Theory (ISIT)Jul 1, 20132 citations

Analysis of stopping constellation distribution for irregular non-binary LDPC code ensemble

T. Nozaki, Kenta Kasai, Kohichi Sakaniwa

The fixed points of the belief propagation decoder for non-binary low-density parity-check (LDPC) codes are referred to as stopping constellations. In this paper, we give the stopping constellation distributions for the irregular non-binary LDPC code ensembles defined over the general linear group. Moreover, we derive the exponential growth rate of the average number of the stopping constellation distributions in the limit of large code length.

IEEE International Symposium on Information Theory (ISIT)Jul 1, 20114 citations

On the weight and stopping set size distributions of LDPC codes and their generalizations

Mark F. Flanagan, Enrico Paolini

This paper overviews and connects together recent results by the authors regarding the weight and stopping set size distributions of generalizations of low-density parity-check (LDPC) codes. We begin by reviewing a result which allows for evaluation of the growth rate of the weight distribution for codewords of any weight (linear in the codeword length). We then show how asymptotic analysis of this general result can lead to a result which encapsulates the behaviour of the growth rate of the weight distribution for the case of small linear-weight codewords. We then show that many existing results in the literature along this line may be viewed as special cases of this general result.

International Symposium on Applied Sciences in Biomedical and Communication TechnologiesNov 1, 20090 citations