• Journal of Communications and Networks
• /
• v.15 no.1
• /
• pp.71-76
• /
• 2013

A new class of quantum low-density parity-check (LDPC) codes whose parity-check matrices are dual-containing matrices constructed based on lines of Euclidean geometries (EGs) is presented. The parity-check matrices of our quantum codes contain one and only one 4-cycle in every two rows and have better distance properties. However, the classical parity-check matrix constructed from EGs does not satisfy the condition of dual-containing. In some parameter conditions, parts of the rows in the matrix maybe have not any nonzero element in common. Notably, we propose four families of fascinating structure according to changes in all the parameters, and the parity-check matrices are adopted to satisfy the requirement of dual-containing. Series of matrix properties are proved. Construction methods of the parity-check matrices with dual-containing property are given. The simulation results show that the quantum LDPC codes constructed by this method perform very well over the depolarizing channel when decoded with iterative decoding based on the sum-product algorithm. Also, the quantum codes constructed in this paper outperform other quantum codes based on EGs.

• Journal of Communications and Networks
• /
• v.13 no.3
• /
• pp.205-210
• /
• 2011

This paper presents an approach to the construction of multiple-rate quasi-cyclic low-density parity-check (LDPC) codes. Parity-check matrices of the proposed codes consist of $q{\times}q$ square submatrices. The block rows and block columns of the parity-check matrix correspond to the hyperplanes (${\mu}$-fiats) and points in Euclidean geometries, respectively. By decomposing the ${\mu}$-fiats, we obtain LDPC codes of different code rates and a constant code length. The code performance is investigated in term of the bit error rate and compared with those of LDPC codes given in IEEE standards. Simulation results show that our codes perform very well and have low error floors over the additive white Gaussian noise channel.

• ETRI Journal
• /
• v.29 no.3
• /
• pp.381-389
• /
• 2007

In this paper we propose a graph-theoretic method based on linear congruence for constructing low-density parity check (LDPC) codes. In this method, we design a connection graph with three kinds of special paths to ensure that the Tanner graph of the parity check matrix mapped from the connection graph is without short cycles. The new construction method results in a class of (3, ${\rho}$)-regular quasi-cyclic LDPC codes with a girth of 12. Based on the structure of the parity check matrix, the lower bound on the minimum distance of the codes is found. The simulation studies of several proposed LDPC codes demonstrate powerful bit-error-rate performance with iterative decoding in additive white Gaussian noise channels.

• Korean Journal of Optics and Photonics
• /
• v.14 no.2
• /
• pp.150-154
• /
• 2003

In this paper, we introduce modified parity coding methods to reduce the errors caused by spatial beam intensity variations in a holographic data storage system. We explained the encoding and decoding process of the conventional parity coding and the modified parity coding techniques. We compared the bit-error-rate (BER) performances of the conventional parity coding and the modified parity coding techniques from experimental evaluation.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.32 no.3C
• /
• pp.205-215
• /
• 2007

This paper presents low latency and/or computation algorithms of iterative codes of turbo codes, turbo product codes and low density parity check codes for use in wireless broadband communication systems. Due to high coding complexity of iterative codes, this paper focus on lower complexity and/or latency algorithms that are easily implementable in hardware and further accelerate the decoding speed.

• ETRI Journal
• /
• v.45 no.3
• /
• pp.404-417
• /
• 2023

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 E_b/N₀ than conventional LDPC codes, which showed a BER of 10^-7 at 3 dB E_b/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 dB E_b/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.

• Journal of Communications and Networks
• /
• v.17 no.4
• /
• pp.346-350
• /
• 2015

It is known that the progressive edge-growth (PEG) algorithm can be used to construct low-density parity-check (LDPC) codes at finite code lengths with large girths through the establishment of edges between variable and check nodes in an edge-by-edge manner. In [1], the authors derived a class of LDPC codes for relay communication systems by extending the full-diversity root-LDPC code. However, the submatrices of the parity-check matrix H corresponding to this code were constructed separately; thus, the girth of H was not optimized. To solve this problem, this paper proposes a modified PEG algorithm for use in the design of large girth and full-diversity LDPC codes. Simulation results indicated that the LDPC codes constructed using the modified PEG algorithm exhibited a more favorable frame error rate performance than did codes proposed in [1] over block-fading channels.

• Journal of Communications and Networks
• /
• v.11 no.5
• /
• pp.455-463
• /
• 2009

We consider the challenges of finding good puncturing patterns for rate-compatible low-density parity-check code (LDPC) codes over additive white Gaussian noise (AWGN) channels. Puncturing is a scheme to obtain a series of higher rate codes from a lower rate mother code. It is widely used in channel coding but it causes performance is lost compared to non-punctured LDPC codes at the same rate. Previous work, considered the role of survived check nodes in puncturing patterns. Limitations, such as single survived check node assumption and simulation-based verification, were examined. This paper analyzes the performance according to the role of multiple survived check nodes and multiple dead check nodes. Based on these analyses, we propose new algorithm to find a good puncturing pattern for LDPC codes over AWGN channels.

• Journal of Communications and Networks
• /
• v.17 no.4
• /
• pp.328-338
• /
• 2015

Three areas of ongoing research in channel coding are surveyed, and recent developments are presented in each area: Spatially coupled low-density parity-check (LDPC) codes, nonbinary LDPC codes, and polar coding.

• Journal of Communications and Networks
• /
• v.17 no.4
• /
• pp.351-361
• /
• 2015

In this paper, a new decoding scheme is proposed to improve the error correcting performance of low-density parity-check (LDPC) codes in high signal-to-noise ratio (SNR) region by using post-processing. It behaves as follows: First, a conventional LDPC decoding is applied to received LDPC codewords one by one. Then, we count the number of word errors in a predetermined number of decoded codewords. If there is no word error, nothing needs to be done and we can move to the next group of codewords with no delay. Otherwise, we perform a proper post-processing which produces a new soft-valued codeword (this will be fully explained in the main body of this paper) and then apply the conventional LDPC decoding to it again to recover the unsuccessfully decoded codewords. For the proposed decoding scheme, we adopt a simple product code structure which contains LDPC codes and simple algebraic codes as its horizontal and vertical codes, respectively. The decoding capability of the proposed decoding scheme is defined and analyzed using the parity-check matrices of vertical codes and, especially, the combined-decodability is derived for the case of single parity-check (SPC) codes and Hamming codes used as vertical codes. It is also shown that the proposed decoding scheme achieves much better error correcting capability in high SNR region with little additional decoding complexity, compared with the conventional LDPC decoding scheme.