(5, k) regular LDPC codes using novel code-construction

2010 ◽  
Author(s):  
S Anggraeni ◽  
V Jeoti
Keyword(s):  
Ldpc Codes ◽  
Code Construction

scholarly journals Overcoming Data Availability Attacks in Blockchain Systems: LDPC Code Design for Coded Merkle Tree

2021 ◽  
Author(s):  
Debarnab Mitra ◽  
Lev Tauz ◽  
Lara Dolecek
Keyword(s):  
Linear Programming ◽  
Ldpc Codes ◽  
Sampling Strategy ◽  
Ldpc Code ◽  
Probability Of Detection ◽  
Data Availability ◽  
Malicious Node ◽  
Code Construction ◽  
Stopping Sets ◽  
Stopping Set

<div>In blockchain systems, full nodes store the entire blockchain ledger and validate all transactions in the system by operating on the entire ledger. However, for better scalability and decentralization of the system, blockchains also run light nodes that only store a small portion of the ledger. In blockchain systems having a majority of malicious full nodes, light nodes are vulnerable to a data availability (DA) attack. In this attack, a malicious node makes the light nodes accept an invalid block by hiding the invalid portion of the block from the nodes in the system. Recently, a technique based on LDPC codes called Coded Merkle Tree (CMT) was proposed by Yu et al. that enables light nodes to detect a DA attack by randomly requesting/sampling portions of the block from the malicious node. However, light nodes fail to detect a DA attack with high probability if a malicious node hides a small stopping set of the LDPC code. To mitigate this problem, Yu et al. used well-studied techniques to design random LDPC codes with high minimum stopping set size. Although effective, these codes are not necessarily optimal for this application. In this paper, we demonstrate that a suitable co-design of specialized LDPC codes and the light node sampling strategy can improve the probability of detection of DA attacks. We consider different adversary models based on their computational capabilities of finding stopping sets in LDPC codes. For a weak adversary model, we devise a new LDPC code construction termed as the entropy-constrained PEG (EC-PEG) algorithm which concentrates stopping sets to a small group of variable nodes. We demonstrate that the EC-PEG algorithm coupled with a greedy sampling strategy improves the probability of detection of DA attacks. For stronger adversary models, we provide a co-design of a sampling strategy called linear-programming-sampling (LP-sampling) and an LDPC code construction called linear-programming-constrained PEG (LC-PEG) algorithm. The new co-design demonstrates a higher probability of detection of DA attacks compared to approaches proposed in earlier literature.</div>

scholarly journals Constructing High-Rate QC-LDPC Codes with Large-Girth based on Shortened Array Codes

2011 ◽  
Vol 1 (03) ◽  
Author(s):  
Xu Chen ◽  
Francis C. M. Lau
Keyword(s):  
Ldpc Codes ◽  
High Rate ◽  
Minimum Length ◽  
Low Density ◽  
Parity Check ◽  
Error Performance ◽  
Code Construction ◽  
Array Codes ◽  
Low Density Parity Check ◽  
Large Girth

In this paper, we aim at constructing high-rate quasi-cyclic low-density parity-check (QC-LDPC) codes with girth-10 based on shortened array codes. Our first contribution is the derivation of analytic results on the maximum number of columns for shortened array codes of different girths. Then, inspired by the analysis, we propose a code construction method for column-weight-three codes. We further compare the minimum length and the error performance of the column-weight-three codes constructed by the proposed algorithm and those found by the conventional greedy construction algorithm. We show that the proposed method is more effective than the conventional greedy algorithm in the sense that the minimum length of the codes constructed using the proposed method to achieve different code rates is comparative or much shorter than those constructed using the greedy construction.

scholarly journals Development of Niederriter crypto-code design models on LDPC-codes

2021 ◽  
pp. 58-68
Author(s):  
С.С. Погасій ◽  
С.В. Мілевський ◽  
О.С. Жученко ◽  
Б.П. Томашевський ◽  
І.Р. Рагімова ◽  
...  
Keyword(s):  
Wireless Networks ◽  
Ieee 802.15.4 ◽  
Quantum Computer ◽  
Ldpc Codes ◽  
Sharp Decrease ◽  
Social Engineering ◽  
Mobile Internet ◽  
Mobile Technologies ◽  
Code Design ◽  
Code Construction

The development of mobile technologies and computing resources has expanded the range of digital services and practically outstripped the development of computer technologies. This approach ensures the use of mobile and wireless networks in almost all areas of smart technologies, provides a further synthesis of cyberspace and the mobile Internet. However, the absence of security service protocols: confidentiality and integrity, initially when they are formed in the structure of LTE technologies, provides cyber attackers with the opportunity to use mobile Internet channels to implement targeted (APT) attacks. The development and emergence of a full-scale quantum computer with Shor and Grover algorithms can lead to a sharp decrease in the level of security of cryptosystems based on symmetric and asymmetric cryptography (including cryptography on elliptic curves). In addition, modern cyber threats have signs of synergy and hybridity, and their integration with social engineering methods practically does not allow providing the required level of preventive measures (protection). The article proposes post-quantum cryptosystems based on the Niederreiter crypto-code construction on low-density parity-check codes (LDPC-codes). This approach makes it easy to integrate into wireless networks based on IEEE 802.16 and IEEE 802.15.4 standards, as well as LTE mobile technologies. At the same time, the required level of resistance to modern threats ensured.

scholarly journals Overcoming Data Availability Attacks in Blockchain Systems: LDPC Code Design for Coded Merkle Tree

2021 ◽  
Author(s):  
Debarnab Mitra ◽  
Lev Tauz ◽  
Lara Dolecek
Keyword(s):  
Linear Programming ◽  
Ldpc Codes ◽  
Sampling Strategy ◽  
Ldpc Code ◽  
Probability Of Detection ◽  
Data Availability ◽  
Malicious Node ◽  
Code Construction ◽  
Stopping Sets ◽  
Stopping Set

<div>In blockchain systems, full nodes store the entire blockchain ledger and validate all transactions in the system by operating on the entire ledger. However, for better scalability and decentralization of the system, blockchains also run light nodes that only store a small portion of the ledger. In blockchain systems having a majority of malicious full nodes, light nodes are vulnerable to a data availability (DA) attack. In this attack, a malicious node makes the light nodes accept an invalid block by hiding the invalid portion of the block from the nodes in the system. Recently, a technique based on LDPC codes called Coded Merkle Tree (CMT) was proposed by Yu et al. that enables light nodes to detect a DA attack by randomly requesting/sampling portions of the block from the malicious node. However, light nodes fail to detect a DA attack with high probability if a malicious node hides a small stopping set of the LDPC code. To mitigate this problem, Yu et al. used well-studied techniques to design random LDPC codes with high minimum stopping set size. Although effective, these codes are not necessarily optimal for this application. In this paper, we demonstrate that a suitable co-design of specialized LDPC codes and the light node sampling strategy can improve the probability of detection of DA attacks. We consider different adversary models based on their computational capabilities of finding stopping sets in LDPC codes. For a weak adversary model, we devise a new LDPC code construction termed as the entropy-constrained PEG (EC-PEG) algorithm which concentrates stopping sets to a small group of variable nodes. We demonstrate that the EC-PEG algorithm coupled with a greedy sampling strategy improves the probability of detection of DA attacks. For stronger adversary models, we provide a co-design of a sampling strategy called linear-programming-sampling (LP-sampling) and an LDPC code construction called linear-programming-constrained PEG (LC-PEG) algorithm. The new co-design demonstrates a higher probability of detection of DA attacks compared to approaches proposed in earlier literature.</div>

A Novel Quasi-Cyclic LDPC Codes Construction Method for High-Speed Parallel Decoding

2013 ◽  
Vol 347-350 ◽  
pp. 3702-3707
Author(s):  
Ming Ke Dong ◽  
Da Wang ◽  
Ya Dan Zheng ◽  
Shang Zhu Wu ◽  
Hai Ge Xiang
Keyword(s):  
High Speed ◽  
Block Size ◽  
Ldpc Codes ◽  
Ldpc Code ◽  
Data Access ◽  
Construction Method ◽  
Parity Check ◽  
Code Construction ◽  
Low Density Parity Check ◽  
Efficient Decoding

The decoding parallelism of quasi-cyclic low density parity check (QC-LDPC) codes, an important realization factor of LDPC codes, is limited by the block size. Joint row-column (JRC) decoding algorithm, an efficient decoding technique having low computation cost and small iteration number, also suffers from the decoding parallelism limitation in QC-LDPC application. In this paper, a novel LDPC-code construction method is presented and validated. This method constructs the row sets to eliminate the data access conflicts, and it clearly enhances the decoding parallelism while avoids any degradation of bit error rate (BER) performance.

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