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This paper proposed a novel method for constructing quasi-cyclic low-density parity-check (QC-LDPC) codes of medium to high code rates that can be applied in cloud data storage systems, requiring better error correction capabilities. The novelty of this method lies in the construction of sparse base matrices, using a girth greater than 4 that can then be expanded with a lift factor to produce high code rate QC-LDPC codes. Investigations revealed that the proposed large-sized QC-LDPC codes with high code rates displayed low encoding complexities and provided a low bit error rate (BER) of 10-10 at 3.5 dB Eb/N0 than conventional LDPC codes, which showed a BER of 10-7 at 3 dB Eb/N0. Subsequently, implementation of the proposed QC-LDPC code in a softwaredefined radio, using the NI USRP 2920 hardware platform, was conducted. As a result, a BER of 10-6 at 4.2 Eb/N0 was achieved. Then, the performance of the proposed codes based on their encoding-decoding speeds and storage overhead was investigated when applied to a cloud data storage (GCP). Our results revealed that the proposed codes required much less time for encoding and decoding (of data files having a 10 MB size) and produced less storage overhead than the conventional LDPC and Reed-Solomon codes.

Since their rediscovery in the early 1990s, low-density parity-check (LDPC) codes have become the most popular error-correcting codes owing to their excellent performance. An LDPC code is a linear block code that has a sparse parity-check matrix. Cycles in this matrix, particularly short cycles, degrade the performance of such a code. Hence, several methods for counting short cycles in LDPC codes have been proposed, such as Fan’s method to detect 4-cycles, 6- cycles, 8-cycles, and 10-cycles. Unfortunately, this method fails to count all 6- cycles, i.e., ignores numerous 6-cycles, in some given parity-check matrices. In this paper, an improvement of this algorithm is presented that detects all 6-cycles in LDPC codes, as well as in general bipartite graphs. Simulations confirm that the improved method offers the exact number of 6-cycles, and it succeeds in detecting those ignored by Fan’s method.

Abstract The problem of blind phase offset recovery of low density parity-check (LDPC)-coded systems is considered in this paper. We propose a new algorithm of phase offset estimation that involves the computation and maximization of a likelihood difference (LD)-based cost function calculated from the parity-check matrix of the code. We show in this paper that the new cost function has a simplified form compared to another algorithm proposed in the literature and presents similar estimation performance. Mean squared error (MSE) curves show very good performance of the proposed phase offset estimation algorithm, even at low signal-to-noise ratios.

During the digital transmission of information, errors are bound to occur. The errors may be random or burst errors. In this paper, we have obtained necessary and sufficient conditions for the existence of linear codes over that are capable of correcting -repeated burst errors of length(fixed) and -repeated burst errors of length (fixed) within sub-blocks of unequal lengths. We have also constructed a parity-check matrix for such a code.

Syndrome-Trellis Code (STC) is a near-optimal convolutional method for adaptive steganography. Hitherto, the existing adaptive steganography commonly depends on the carefully designed distortion cost function, which controls the embedding position of the message in the cover signal. From another point of view, we implement adaptive steganography by improving the STC coding process (named Adaptive-STC). The parity-check matrix is the key to the encoding and extraction process of STC. In this work, we prove that the average embedding change probability of corresponding elements can be changed by adjusting its submatrix. Following that, we specially design an adaptive parity-check matrix to replace the designed distortion cost to restrict the embedding position. The generation of the adaptive parity-check matrix can be formulated as a multi-constrained integer programming problem in which the width of the submatrix is allocated at a fixed height. To solve this particular problem, we propose a targeted intelligent optimization algorithm (named GOAS) that can adaptively generate the parity-check matrix according to different audio cover. The experimental results show that the proposed method outperforms the state-of-the-art adaptive steganography with reduced embedding changes and improved audio quality while ensuring the ability against steganalysis.

This paper proposes a new method for building low-density-parity-check codes, exempt of cycle of length 4, based on a circulant permutation matrix, which needs very little memory for storage it in the encoder and a dual diagonal structure is applied to guarantee that parity check bits can be recursively computed with linear calculation complexity. The Bit Error Rate performance of the new low-density-parity-check codes was compared to the uncoded bi-phase-shift-keying over additive-white-gaussian-noise channel. This simulation shows that the proposed codes are very efficient over additive-white-gaussian-noise. The proposed codes ensure a very low encoding complexity and reduce the memory storage required for the parity-check matrix, which can be more easily built than others codes used in channel coding.

In this paper, the parity-check matrices that can be used in low density parity check (LDPC) based error correction method for quantum key distribution are analyzed. The quantum key distribution system has inevitable errors in sifted key that must be corrected by an error correction algorithm to create a secure key. In this analysis, 1000-bit sifted keys are divided into 50 parts. The algorithm creates 50 syndromes corresponding to each part by multiplying 10 × 20 bit parity-check matrices. The algorithm sends the generated syndrome to the other side, which also divides the sifted key into 50 parts, creates a syndrome from each part, and compares with the received syndrome. If the syndromes are different, these sifted key parts are discarded. However, there may be situations where different parts may have the same syndromes. Therefore, it is necessary to find such an optimal matrix that removes the probability of getting the same syndromes at different parts of the sifted key.