Designing LDPC codes using cyclic shifts

Okamura, Toshihiko

doi:10.1109/isit.2003.1228165

Cited by 10 publications

(7 citation statements)

References 3 publications

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“…1 This second approach was initially proposed by Gallager [13, Appendix C] (although in this original construction, the permutation matrices are not restricted to circulants). A special class of these codes was later analyzed in [14] and several recent works consider structured ways to design such codes [15]- [20]. In fact, these two methods are interrelated and, for example, many of the code constructions based on finite geometries have an equivalent circulant permutation matrix representation [21, p. 286].…”

Section: Introductionmentioning

confidence: 99%

Quasi-Cyclic Low-Density Parity-Check Codes From Circulant Permutation Matrices

Fossorier

2004

IEEE Trans. Inform. Theory

1,063

798

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Abstract-In this correspondence, the construction of low-density parity-check (LDPC) codes from circulant permutation matrices is investigated. It is shown that such codes cannot have a Tanner graph representation with girth larger than 12, and a relatively mild necessary and sufficient condition for the code to have a girth of 6 8 10 or 12 is derived. These results suggest that families of LDPC codes with such girth values are relatively easy to obtain and, consequently, additional parameters such as the minimum distance or the number of redundant check sums should be considered. To this end, a necessary condition for the codes investigated to reach their maximum possible minimum Hamming distance is proposed.

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Section: Introductionmentioning

confidence: 99%

Quasi-Cyclic Low-Density Parity-Check Codes From Circulant Permutation Matrices

Fossorier

2004

IEEE Trans. Inform. Theory

1,063

798

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“…Four cycles are illustrated as a tanner graph in the following Figure 2 as a general example. In the papers [16,18,33], some methods for memory-efficient construction of parity check matrices have been demonstrated. Gallagar, in his paper [4] has introduced a specific construction method for regular LDPC codes as shown in Equations (7) and (8) .…”

Section: Ldpc Code Structurementioning

confidence: 99%

“…Methods of algebraic construction are used to construct cyclic or quasi-cyclic LDPC codes with combination methods. This structured LDPC codes [16][17][18], in general, are simple to encode and decode as compared with the random codes. The LDPC codes have shown the capacity approaching performance, but at the expense of high complexity which is the main hurdle to be adopted, these codes in many real-world applications and implementations.…”

mentioning

confidence: 99%

A New Construction of High Performance LDPC Matrices for Mobile Networks

Sarvaghad-Moghaddam

Ullah

Jayakody

et al. 2020

Sensors

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Secure and reliable information flow is one of the main challenges in social IoT and mobile networks. Information flow and data integrity is still an open research problem. In this paper, we develop new methods of constructing systematic and regular Low-Density Parity-Check Matrices (LDPCM), inspired by the structure of the Sarrus method and geometric designs. Furthermore, these codes have cyclic structure and therefore, are less complex in computation and also require less memory in hardware implementation. Besides, an optimal method of post-processing for deleting girths four is presented. Numerical results show that the codes constructed by these methods perform well over the additive white Gaussian noise (AWGN) channel when decoded with the sum-product LDPC iterative algorithms. The proposed methods can be very efficient in terms of reducing memory consumption and improving the convergence speed of the decoder particularly in IoT and mobile networks. of 24gained attention recently and substantial research work has been done in designing the parity check matrices, low complexity encoding and decoding algorithms and numerous practical applications [7][8][9][10][11][12].The bit error performance of the LDPC code primarily depends on the construction [13] of LDPCM and on parameters such as row and column weights, rate, girth, and code size. Constructions of LDPCM can be categorized into two broad groups: random (irregular) and algebraic constructions (regular). The computer search method is generally used for random construction of LDPCM with a predefined set of design rules based on the Tanner graphs [14] which gives connectivity of the bit (variable) nodes and the check nodes. Randomly constructed irregular LDPC codes can perform within 0.0045 dB of Shannon limit [15] but these codes are very complex to implement in hardware. Methods of algebraic construction are used to construct cyclic or quasi-cyclic LDPC codes with combination methods. This structured LDPC codes [16][17][18], in general, are simple to encode and decode as compared with the random codes. The LDPC codes have shown the capacity approaching performance, but at the expense of high complexity which is the main hurdle to be adopted, these codes in many real-world applications and implementations. Recently LDPC codes have been adopted by digital video broadcasting and IEEE standards like DVB-S2, DVB-X2, WiFI and WiMax [19,20]. Case Study LDPC User Cases in 5GCellular networks and the Internet of Things are the main market drivers for 5G and beyond. There is a large number of use cases for cellular networks and the Internet of Things, such as virtual reality, augmented reality and remote sensing, eHealth services, automotive driving and many more.Keeping in view the IoT enabled devices, 5G is meant to operate at higher speeds and make the delay nearly non-existent, giving way to a seamless information flow [21]. Mobile IoT-based devices offer the low-cost, low-power consumption solution in comparison with the existing 4G. This 5G enabled mobile netw...

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“…We describe it completely for the first situation. We pick a length-six ordered series O equal to (18), i.e., O = {(j, l), (j, l), (j, l), (j, l), (j, l), (j, l)}, where (j, l) is the index of the labeled tree T j,l that has three leaves. Let the three length-K coefficient vectors correspond to the three leaves be s a , s b , s c and select the coefficient set S = {s a , s b , s c , s a , s b , s c }.…”

Section: Inevitable Cycles In Hqc Ldpc Codesmentioning

confidence: 99%

“…In the past, QC LDPC codes have been constructed based on a wide variety of mathematical ideas, including finite geometries, finite fields, and combinatorial designs [2], [12]- [18]. Recently, there has also been great interest in the class of "convolutional" [19], [20] or "spatially-coupled" [21] LDPC codes.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical and High-Girth QC LDPC Codes

Wang

Draper

Yedidia

2013

IEEE Trans. Inform. Theory

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Abstract-We present a general approach to designing capacity-approaching high-girth low-density parity-check (LDPC) codes that are friendly to hardware implementation. Our methodology starts by defining a new class of hierarchical quasicyclic (HQC) LDPC codes that generalizes the structure of quasicyclic (QC) LDPC codes. Whereas the parity check matrices of QC LDPC codes are composed of circulant sub-matrices, those of HQC LDPC codes are composed of a hierarchy of circulant sub-matrices that are in turn constructed from circulant submatrices, and so on, through some number of levels. We show how to map any class of codes defined using a protograph into a family of HQC LDPC codes. Next, we present a girth-maximizing algorithm that optimizes the degrees of freedom within the family of codes to yield a high-girth HQC LDPC code. Finally, we discuss how certain characteristics of a code protograph will lead to inevitable short cycles, and show that these short cycles can be eliminated using a "squashing" procedure that results in a high-girth QC LDPC code, although not a hierarchical one. We illustrate our approach with designed examples of girth-10 QC LDPC codes obtained from protographs of one-sided spatiallycoupled codes.

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Designing LDPC codes using cyclic shifts

Cited by 10 publications

References 3 publications

Quasi-Cyclic Low-Density Parity-Check Codes From Circulant Permutation Matrices

Quasi-Cyclic Low-Density Parity-Check Codes From Circulant Permutation Matrices

A New Construction of High Performance LDPC Matrices for Mobile Networks

Hierarchical and High-Girth QC LDPC Codes

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