We present a novel construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes with arbitrary column weight and girth at least eight. By carefully designing the parity-check matrix, our approach ensures both structural flexibility and improved error-correction capabilities. We evaluate the performance of these codes under the additive white Gaussian noise (AWGN) channel. Simulation results demonstrate that the proposed QC-LDPC codes outperform the protograph LDPC codes included in the Consultative Committee for Space Data Systems (CCSDS) telecommand standards. Additionally, we benchmark our proposed codes against existing short-length codes with girth 8, observing improvements in the decoding performance while ensuring suitability for hardware implementation. The findings of this work contribute to the ongoing development of efficient LDPC codes suitable for ultra-reliable low-latency communications and area-efficient architecture designs for the Internet of Things (IoT), machine-to-machine (M2M), and satellite communications.
We present a novel construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes with arbitrary column weight and girth at least eight. By carefully designing the parity-check matrix, our approach ensures both structural flexibility and improved error-correction capabilities. We evaluate the performance of these codes under the additive white Gaussian noise (AWGN) channel. Simulation results demonstrate that the proposed QC-LDPC codes outperform the protograph LDPC codes included in the Consultative Committee for Space Data Systems (CCSDS) telecommand standards. Additionally, we benchmark our proposed codes against existing short-length codes with girth 8, observing improvements in the decoding performance while ensuring suitability for hardware implementation. The findings of this work contribute to the ongoing development of efficient LDPC codes suitable for ultra-reliable low-latency communications and area-efficient architecture designs for the Internet of Things (IoT), machine-to-machine (M2M), and satellite communications.
We present a novel construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes with arbitrary column weight and girth at least eight. Furthermore, we demonstrate that in the case of column weight three, the absorbing sets (3, 3) and (4, 2) can be entirely avoided in our construction, resulting in improved code performance. Building on the strong performance of our constructed QC-LDPC codes, we extend them to design several families of spatially coupled (SC) QC-LDPC codes, which further enhance decoding performance under windowed decoding. Simulation results under the additive white Gaussian noise (AWGN) channel demonstrate that the proposed QC-LDPC codes outperform the LDPC codes part of the space data systems standards. Additionally, we benchmark our proposed QC-LDPC and SC-QC-LDPC codes against existing girth-8 codes, observing significant improvements in the decoding performance of SC-QC-LDPC codes up to 1.1 dB compared to the protographbased construction by Shiyun Mo et al. [IEEE Trans. Commun.], while maintaining suitability for hardware implementation. The findings of this work contribute to the ongoing development of efficient LDPC codes suitable for ultra-reliable low-latency communications and area-efficient architecture designs.
We present a novel construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes with arbitrary column weight and girth at least eight. Furthermore, we demonstrate that in the case of column weight three, the absorbing sets (3, 3) and (4, 2) can be entirely avoided in our construction, resulting in improved code performance. Building on the strong performance of our constructed QC-LDPC codes, we extend them to design several families of spatially coupled (SC) QC-LDPC codes, which further enhance decoding performance under windowed decoding. Simulation results under the additive white Gaussian noise (AWGN) channel demonstrate that the proposed QC-LDPC codes outperform the LDPC codes part of the space data systems standards. Additionally, we benchmark our proposed QC-LDPC and SC-QC-LDPC codes against existing girth-8 codes, observing significant improvements in the decoding performance of SC-QC-LDPC codes up to 1.1 dB compared to the protographbased construction by Shiyun Mo et al. [IEEE Trans. Commun.], while maintaining suitability for hardware implementation. The findings of this work contribute to the ongoing development of efficient LDPC codes suitable for ultra-reliable low-latency communications and area-efficient architecture designs.
There is an important breakthrough in the field of forward error correction techniques, low-density parity-check (LDPC) codes. These codes have potential to approach the Shannon limit with reliable performance on a given channel, known as the channel capacity. Recently, researchers pay much more attention towards LDPC codes because its performance is better than Turbo codes. However, the LDPC code is the best when it is an irregular code and uses with a very large block-length. Although, the short block-length LDPC codes perform not so well, they are easy to implement in various practical applications. Therefore, there is still a demand of new development on the encoding side of LDPC codes for various ranges of code rate and code length so as to capable of using in many applications.This thesis proposes the development of quasi-cyclic (QC) LDPC codes for column weight 3. In the first part of this thesis, we propose a new construction algorithm of QC-LDPC codes for medium to large block-length by combining QC-LDPC codes of small block-length as their component codes, via Chinese remainder theorem (CRT). Such component codes were constructed by permuting each column block sequentially to attain the desire local girth. After combining all component codes to generate an expanded parity-check matrix, the resulting girth is greater than or at least equal to the maximum girth of the component codes. Simulation results show that our proposed construction method of the parity-check matrix significantly outperforms the other well-known existing methods in terms of low error-floor, simple structure, high performance, and can reduce encoding complexity.In addition, this thesis also proposes two new construction methods for QC-LDPC codes, namely a base matrix method and a subtraction based method. A base matrix based method is a simple, less computational complexity method for constructing the exponent matrix (3, K) of girth 8, 10 and 12 of QC-LDPC codes. Another method is a subtraction method, which has a similar exponent matrix as a base matrix method and has a girth at least 8. Results indicate that the LDPC codes constructed from these two methods have flexibility for arbitrary block-column length K and have a similar BER performance if compared to existing methods.
This study proposes an explicit construction method for quantum quasi-cyclic low-density parity-check (QC-LDPC) codes with a girth of 12. The proposed method designs parity-check matrices that maximize the girth while maintaining an orthogonal structure suitable for quantum error correction. By utilizing algebraic techniques, short cycles are eliminated, which improves error correction performance. Additionally, this method is extended to non-binary LDPC codes and spatially-coupled LDPC codes, demonstrating that both the girth and orthogonality can be preserved. The results of this study enable the design of high-performance quantum error-correcting codes without the need for random search.
Quasi-cyclic low-density parity-check (QC-LDPC) codes are known to have algebraic structure, which suits hardware implementation. However, low girth makes their performances worse than random structured LDPC codes. Based on independent row-column mapping sequence, this work proposed a generalized method of constructing QC-LDPC codes with girth eight, which enlarges the class of girth eight QC-LDPC codes to a fairly general series. Simulation results show that the bit error rate of the constructed codes is close to that of progressive edge growth (PEG) based QC-LDPC codes under iterative decoding.
Multitype quasi-cyclic (QC) low-density parity-check (LDPC) codes are a class of protograph LDPC codes lifted cyclically from protographs with multiple edges, represented by two weight and slope matrices. For a given weight-matrix, an approach is proposed to find the maximum-achievable girthgmaxof the corresponding multitype QC-LDPC codes by some inevitable chains having less complexity than the existing methods. This advantage leads to some new patterns of the weight matrices such that the corresponding codes have some improvements in terms of the maximum-achievable girths or the minimum-distance upper-bounds. In continue, for a given weight-matrix with maximum-achievable girthgmax, some slope-matrices are constructed by a depth-first search algorithm for which the corresponding multitype QC-LDPC codes with even girthg,g≤gmax, have smaller lengths, higher rates, or larger minimum-distances than the state-of-the-art achievements. Simulation results show that the constructed codes have some error-rate advantages than PEG, random-like, CCSDS, and 802.11n/ac IEEE standard LDPC codes.