Error floors of non-binary LDPC codes

Nozaki, Takayuki; Kasai, Kazuhiko; Sakaniwa, Kohichi

doi:10.1109/isit.2010.5513602

Cited by 6 publications

(6 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Codes with efficient encoding and decoding were proposed in [52]. The error-floor performance of non-binary LDPC codes was recently investigated in [36] and [38], and non-codeword objects that cause the decoding error under iterative decoding were studied in [37] and [41]. Minimum distance properties of non-binary LDPC codes were recently explored in [29].…”

Section: Introductionmentioning

confidence: 99%

Non-Binary Protograph-Based LDPC Codes: Enumerators, Analysis, and Designs

Dolecek

Divsalar

Sun

et al. 2014

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

Abstract-This paper provides a comprehensive analysis of non-binary low-density parity check (LDPC) codes built out of protographs. We consider both random and constrained edgeweight labeling, and refer to the former as the unconstrained non-binary protograph-based LDPC codes (U-NBPB codes) and the latter as the constrained non-binary protograph-based LDPC codes (C-NBPB codes). Equipped with combinatorial definitions extended to the non-binary domain, ensemble enumerators of codewords, trapping sets, stopping sets, and pseudocodewords are calculated. The exact enumerators are presented in the finite-length regime, and the corresponding growth rates are calculated in the asymptotic regime. We then present an EXIT chat tool for computing the iterative decoding thresholds of protograph-based LDPC codes followed by several examples of finite-length U-NBPB and C-NBPB codes with high performance. Throughout the paper, we provide accompanying examples which demonstrate the advantage of non-binary protograph-based LDPC codes over their binary counterparts and over random constructions. The results presented in this paper advance the analytical toolbox of non-binary graph-based codes.

show abstract

Section: Introductionmentioning

confidence: 99%

Non-Binary Protograph-Based LDPC Codes: Enumerators, Analysis, and Designs

Dolecek

Divsalar

Sun

et al. 2014

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

show abstract

“…Define Hence, β is not a member of the proper subfield of order 2 r . Thus, we have E (1) β is not equal to the proper subfield of order 2 r for any positive integer r such that r | m and r m. Therefore, we obtain E (1) β = F 2 m . Lemma 5: Let E β denote the set of stopping states for β.…”

Section: Appendix: Proof Of Theoremmentioning

confidence: 94%

“…To prove Theorem 1, we give several lemmas in the following sections. r [17, p.45], where r is a positive integer such that r | m and r m. We will prove E (1) β is not equal to any proper subfields of order 2 r . Define Hence, β is not a member of the proper subfield of order 2 r .…”

Section: Appendix: Proof Of Theoremmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of Error Floors of Non-binary LDPC Codes over BEC

Nozaki

Kasai

Sakaniwa

2012

IEICE Trans. Fundamentals

Self Cite

View full text Add to dashboard Cite

Takayuki NOZAKI†a) , Student Member, Kenta KASAI †b) , Member, and Kohichi SAKANIWA †c) , Fellow SUMMARYIn this paper, we investigate the error floors of the nonbinary low-density parity-check codes transmitted over the binary erasure channels under belief propagation decoding. We propose a method to improve the decoding erasure rates in the error floors by optimizing labels in zigzag cycles in the Tanner graphs of codes. Furthermore, we give lower bounds on the bit and the symbol erasure rates in the error floors. The simulation results show that the presented lower bounds are tight for the codes designed by the proposed method.

show abstract

“…In [6], we analyze the decoding erasure rate in the error floors of non-binary LDPC codes over the binary erasure channel (BEC) under BP decoding. In this paper, we analyze the error floors of non-binary LDPC codes over the MBIOS channel.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Error Floors of Non-Binary LDPC Codes over MBIOS Channel

Nozaki

Kasai

Sakaniwa

2011

2011 IEEE International Conference on Communications (ICC)

Self Cite

View full text Add to dashboard Cite

In this paper, we investigate the error floors of non-binary low-density parity-check (LDPC) codes transmitted over the memoryless binary-input output-symmetric (MBIOS) channels. We provide a necessary and sufficient condition for successful decoding of zigzag cycle codes over the MBIOS channel by the BP decoder. We consider an expurgated ensemble of nonbinary LDPC codes by using this condition, and hence exhibit lower error floors. to analyze and to lower the decoding error rate in the error floor by using the above condition. Finally, we show lower bounds of the error floors for the expurgated LDPC code ensembles over the MBIOS channel.

show abstract

Error floors of non-binary LDPC codes

Cited by 6 publications

References 13 publications

Non-Binary Protograph-Based LDPC Codes: Enumerators, Analysis, and Designs

Non-Binary Protograph-Based LDPC Codes: Enumerators, Analysis, and Designs

Analysis of Error Floors of Non-binary LDPC Codes over BEC

Analysis of Error Floors of Non-Binary LDPC Codes over MBIOS Channel

Contact Info

Product

Resources

About