Results on Punctured Low-Density Parity-Check Codes and Improved Iterative Decoding Techniques

Abstract

Abstract-This paper first introduces an improved decoding algorithm for low-density parity-check (LDPC) codes over binaryinput-output-symmetric memoryless channels. Then some fundamental properties of punctured LDPC codes are presented. It is proved that for any ensemble of LDPC codes, there exists a puncturing threshold. It is then proved that for any rates R1 and R2 satisfying 0 < R1 < R2 < 1, there exists an ensemble of LDPC codes with the following property. The ensemble can be punctured from rate R1 to R2 resulting in asymptotically good codes for all rates R1 R R2. Specifically, this implies that rates arbitrarily close to one are achievable via puncturing. Bounds on the performance of punctured LDPC codes are also presented. It is also shown that punctured LDPC codes are as good as ordinary LDPC codes. For BEC and arbitrary positive numbers R 1 < R 2 < 1, the existence of the sequences of punctured LDPC codes that are capacity-achieving for all rates R 1 R R 2 is shown. Based on the above observations, a method is proposed to design good punctured LDPC codes over a broad range of rates. Finally, it is shown that the results of this paper may be used for the proof of the existence of the capacity-achieving LDPC codes over binary-input-outputsymmetric memoryless channels.

An Iterative Algorithm for Trust Management and Adversary Detection for Delay-Tolerant Networks

“…Further, we evaluated ITRM against some sophisticated attacks (which utilizes bad mouthing or ballot stuffing with a strategy) such as RepTrap [28] or the one in which malicious raters provide both reliable and malicious ratings to mislead the algorithm. Our proposed iterative algorithm is inspired by the earlier work on the improved iterative decoding algorithm of LDPC codes in the presence of stopping sets [4], [29]. In iterative decoding of LDPC, every check vertex (in the graph representation of the code) has some opinion of what the value of each bit vertex should be.…”

“…To achieve this goal, we aim at obtaining a reputation-based trust management system and an iterative malicious node detection mechanism for DTNs. Our work on reputation systems stems from the prior success of iterative algorithms, such as message passing techniques [3] in the decoding of Low-Density Parity-Check (LDPC) codes in erasure channels [4]. We believe the significant benefits offered by iterative algorithms can be tapped in to benefit the field of reputation systems.…”

Design of Finite-Length Generalized LDPC Codes

“…7.11. Another possible reason is that the IRA-DGLDPC code is built by GR-SCNfirst-PEG, the constraints imposed by GR-SCNfirst-PEG make it more like a "multi-edge type" code, it is possible that it has a poor cutoff puncturing rate [56] which results in poor performance at high rates. The last explanation is that the proposed systematic puncturing algorithm still has room for improving, this speculation is also supported by the small gap between systematic puncturing and random puncturing curves in Fig.…”

“…In existing studies, RC-LDPC codes are widely studied in [54][55][56][57][58][59][60][61][62][63][64][65][66], nevertheless there are few studies on RC-GLDPC and RC-DGLDPC codes, making it an unexplored research area.…”

“…Such analysis nonetheless does not describe in detail how the specific bits should be punctured. In [56] it is proved that there is a cutoff rate for the punctured profile such that if the punctured rate is lower than the cutoff rate, the error free of decoding can be achieved via a high-enough SNR, otherwise the error rate is always positive unless the channel is noiseless. Finally, the performance of infinite-length punctured LDPC codes under ML decoding is studied in [58].…”