Minimum Distance and Trapping Set Analysis of Protograph-Based LDPC Convolutional Codes

Mitchell, David G. M.; Pusane, Alí Emre; Costello, Daniel J.

doi:10.1109/tit.2012.2211995

Cited by 56 publications

(87 citation statements)

References 43 publications

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“…To obtain d min = 8, we see from Table I that it is necessary to increase the pre-lifting factor to at least m = 2. It is known that the shortest possible (optimal) (2, 3)-regular code has parameters [45,16,8] [38], which is not too far from the pre-lifted [54, 19,8] code constructed in Section IV-A-1 with m = 2 and r = 9 (which was obtained with no particular effort to minimize block length).…”

Section: ) Discussionmentioning

confidence: 99%

Quasi-cyclic LDPC codes based on pre-lifted protographs

Mitchell

Smarandache

Costello

2011

2011 IEEE Information Theory Workshop

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Abstract-Quasi-cyclic low-density parity-check (QC-LDPC) codes based on protographs are of great interest to code designers because analysis and implementation are facilitated by the protograph structure and the use of circulant permutation matrices for protograph lifting. However, these restrictions impose undesirable fixed upper limits on important code parameters, such as minimum distance and girth. In this paper, we consider an approach to constructing QC-LDPC codes that uses a two-step lifting procedure based on a protograph, and, by following this method instead of the usual one-step procedure, we obtain improved minimum distance and girth properties. We also present two new design rules for constructing good QC-LDPC codes using this two-step lifting procedure, and in each case we obtain a significant increase in minimum distance and achieve a certain guaranteed girth compared to one-step circulant-based liftings. The expected performance improvement is verified by simulation results.

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Section: ) Discussionmentioning

confidence: 99%

Quasi-cyclic LDPC codes based on pre-lifted protographs

Mitchell

Smarandache

Costello

2011

2011 IEEE Information Theory Workshop

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“…The asymptotic weight distribution has also been derived for MET LDPC ensembles [25], for IRA ensembles [44], for protograph ensembles [45], for generalizations of LDPC codes [46,47], and for LDPC convolutional codes [48]. Weight distributions have also been evaluated for many finite-length code ensembles; in this case, analysis involves numerical optimization procedures in order to calculate the relevant distributions.…”

Section: Example 12mentioning

confidence: 99%

Low-Density Parity-Check Code Constructions

Flanagan

2014

Academic Press Library in Mobile and Wireless Communications

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“…Since non-binary LDPC codes not only can outperform their binary counterparts in some cases (e.g., for short/moderate codeword length), but also can be seamlessly combined with high-order modulations [37], [63]- [65], protograph LDPC codes have been extended to the non-binary domain recently [66]- [69]. As a further advancement, the protograph framework has been introduced for convolutional codes [70] so as to form the protograph LDPC convolutional codes [71]- [73], which have certain advantages as compared to protograph LDPC codes without increasing complexity. In addition, some other variants of protograph codes, such as protograph-based raptor-like (PBRL) codes and spatially-coupled protographbased (SCPB) codes, have been developed [74]- [78].…”

Section: Introductionmentioning

confidence: 99%

“…2012 He et al [117] First application of protograph codes to JSCC systems. 2013 Mitchell et al [73] Analyzed the minimum distance and trapping set of the protograph-based convolutional codes. 2013 C. A. Kelley [104] Proposed the algebraic protograph codes and their corresponding implementation.…”

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A Survey on Protograph LDPC Codes and Their Applications

Fang

Guan

et al. 2015

IEEE Commun. Surv. Tutorials

147

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Low-density parity-check (LDPC) codes have attracted much attention in the past two decades since they can asymptotically approach the Shannon capacity in a variety of data transmission and storage scenarios. As a type of promising structured LDPC codes, the protograph LDPC codes not only inherit the advantage of conventional LDPC codes, i.e., excellent error performance, but also possess simple representations to realize fast encoding and efficient decoding. This paper provides a comprehensive survey on the state-of-the-art in protograph LDPC code design and analysis for different channel conditions, including the additive white Gaussian noise (AWGN) channels, fading channels, partial response (PR) channels, and Poisson pulse-position modulation (PPM) channels. Moreover, the applications of protograph LDPC codes to joint sourceand-channel coding (JSCC) and joint channel-and-physical-layernetwork coding (JCPNC) are reviewed and studied. In particular, we focus our attention on the encoding design and assume the decoder is implemented by the belief propagation (BP) algorithm. Hopefully, this survey may facilitate the research in this area.

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Minimum Distance and Trapping Set Analysis of Protograph-Based LDPC Convolutional Codes

Cited by 56 publications

References 43 publications

Quasi-cyclic LDPC codes based on pre-lifted protographs

Quasi-cyclic LDPC codes based on pre-lifted protographs

Low-Density Parity-Check Code Constructions

A Survey on Protograph LDPC Codes and Their Applications

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