This letter presents a construction flow for rate-compatible LDPC (RC-LDPC) codes, collaboratively using both extension and splitting schemes. In addition to the decoding threshold used for selecting the degree distribution, a new metric, known as the Average ACE (A2CE) value, is introduced in order to estimate the Tanner graph connectivity. The proposed collaborative scheme provides more flexibility in the designs of the degree distribution and graph connectivity, both of which are critical for RC LDPC codes that have short and/or moderate lengths. The designed LDPC codes achieve a comparable or better error rate performance compared to existing codes.
This letter presents a construction flow for rate-compatible LDPC (RC-LDPC) codes, collaboratively using both extension and splitting schemes. In addition to the decoding threshold used for selecting the degree distribution, a new metric, known as the Average ACE (A2CE) value, is introduced in order to estimate the Tanner graph connectivity. The proposed collaborative scheme provides more flexibility in the designs of the degree distribution and graph connectivity, both of which are critical for RC LDPC codes that have short and/or moderate lengths. The designed LDPC codes achieve a comparable or better error rate performance compared to existing codes.
In this paper, we present an effective puncturing scheme for rate-compatible low-density parity-check (RC-LDPC) codes. Our scheme is based on the criterion of maximum average girth which is an important performance parameter for the construction of RC-LDPC codes. We select a pattern wherein the punctured bits are far apart from each other in the Tanner graph of the codes by sorting algorithm, and then puncture the bits with the maximum average girth. In the process, there is no need to do any optimization. By simulations, the proposed codes show good performance under puncturing over a wide range of rates. The introduced puncturing criterion results in lower bit error rate and error floor when compared with random puncturing. Moreover, the performance of proposed method is similar to the direct structured LDPC codes by progressive edge growth (PEG). But the scheme is very simple to implement and lowers the complexity of encoding and decoding.
In this digital era, modern communication systems play an essential part in nearly every aspect of life, with examples ranging from mobile networks and satellite communications to Internet and data transfer. Unfortunately, all communication systems in a practical setting are noisy, which indicates that we can either improve the physical characteristics of the channel or find a possible systematical solution, i.e. error control coding. The history of error control coding dates back to 1948 when Claude Shannon published his celebrated work “A Mathematical Theory of Communication”, which built a framework for channel coding, source coding and information theory. For the first time, we saw evidence for the existence of channel codes, which enable reliable communication as long as the information rate of the code does not surpass the so-called channel capacity. Nevertheless, in the following 60 years none of the codes have been proven closely to approach the theoretical bound until the arrival of turbo codes and the renaissance of LDPC codes. As a strong contender of turbo codes, the advantages of LDPC codes include parallel implementation of decoding algorithms and, more crucially, graphical construction of codes. However, there are also some drawbacks to LDPC codes, e.g. significant performance degradation due to the presence of short cycles or very high decoding latency. In this thesis, we will focus on the practical realisation of finite-length LDPC codes and devise algorithms to tackle those issues.
Firstly, rate-compatible (RC) LDPC codes with short/moderate block lengths are investigated on the basis of optimising the graphical structure of the tanner graph (TG), in order to achieve a variety of code rates (0.1 < R < 0.9) by only using a single encoder-decoder pair. As is widely recognised in the literature, the presence of short cycles considerably reduces the overall performance of LDPC codes which significantly limits their application in communication systems. To reduce the impact of short cycles effectively for different code rates, algorithms for counting short cycles and a graph-related metric called Extrinsic Message Degree (EMD) are applied with the development of the proposed puncturing and extension techniques. A complete set of simulations are carried out to demonstrate that the proposed RC designs can largely minimise the performance loss caused by puncturing or extension.
Secondly, at the decoding end, we study novel decoding strategies which compensate for the negative effect of short cycles by reweighting part of the extrinsic messages exchanged between the nodes of a TG. The proposed reweighted belief propagation (BP) algorithms aim to implement efficient decoding, i.e. accurate signal reconstruction and low decoding latency, for LDPC codes via various design methods. A variable factor appearance probability belief propagation (VFAP-BP) algorithm is proposed along with an improved version called a locally-optimized reweighted (LOW)-BP algorithm, both of which can be employed to enhance decoding performance significantly for regular and irregular LDPC codes. More importantly, the optimisation of reweighting parameters only takes place in an offline stage so that no additional computational complexity is required during the real-time decoding process.
Lastly, two iterative detection and decoding (IDD) receivers are presented for multiple-input multiple-output (MIMO) systems operating in a spatial multiplexing configuration. QR decomposition (QRD)-type IDD receivers utilise the proposed multiple-feedback (MF)-QRD or variable-M (VM)-QRD detection algorithm with a standard BP decoding algorithm, while knowledge-aided (KA)-type receivers are equipped with a simple soft parallel interference cancellation (PIC) detector and the proposed reweighted BP decoders. In the uncoded scenario, the proposed MF-QRD and VM-QRD algorithms are shown to approach optimal performance, yet require a reduced computational complexity. In the LDPC-coded scenario, simulation results have illustrated that the proposed QRD-type IDD receivers can offer near-optimal performance after a small number of detection/decoding iterations and the proposed KA-type IDD receivers significantly outperform receivers using alternative decoding algorithms, while requiring similar decoding complexity.
Finding coding schemes that approach the Shannon capacity limit has been the central theme during the development of error-control coding (ECC).In recent years low-density parity-check (LDPC) codes, due to their remarkable performance under iterative decoding, have received extensive study and have been adopted by many modern advanced communication systems.LDPC codes can be further extended to generalized LDPC (GLDPC) codes and doublygeneralized LDPC (DGLDPC) codes.GLDPC and DGLDPC codes are supersets of LDPC codes that possess more generic code structures.GLDPC and DGLDPC codes are more flexible than LDPC codes, since a richer variety of check nodes (CNs) or variable nodes (VNs) offers additional options and flexibility, which enable many advantages over LDPC codes in numerous scenarios.In this dissertation we focus on improved design methods for finite-length (FL) GLDPC and DGLDPC codes.The first research topic is the error floor behavior of FL-GLDPC and FL-DGLDPC codes.In GLDPC and DGLDPC codes, the existence of generalized CNs and VNs requires more careful management of edge connections for achieving low error floors.In this work the approximate cycle extrinsic message degree (ACE), a cycle parameter used in LDPC codes that reflects the resilience of the cycle to the noise, is generalized to extended ACE (eACE) for GLDPC and DGLDPC codes.By integrating eACE into the progressive-edge-growth (PEG) algorithm and adding more constraints on the connectivity of nodes, the error floor performance of GLDPC and DGLDPC codes can be greatly improved.In practice, designing codes capable of fast encoding is an important issue.Efficiently-encodable (EE) GLDPC and DGLDPC codes are studied and a self-consistent unified framework is proposed for constructing EE iteratively-decodable block codes, including EE-LDPC, EE-GLDPC and EE-DGLDPC codes.The competing nature of the fast encoding speed and the low error floor performance iv Abstract v is analyzed and verified via various simulation results.EE codes are systematic and suitable for puncturing; therefore, they are good candidates for rate-compatible (RC) data transmissions.Based on the characteristics of GLDPC and DGLDPC codes, we devise several systematic puncturing algorithms to provide good puncturing patterns for them.It is shown that we can significantly improve the code performance compared with random puncturing.Over a wide range of code rates, RC EE-GLDPC and EE-DGLDPC codes show advantages over EE-LDPC codes, especially at high signal-to-noise ratios (SNRs).
Protograph-based Raptor-like low-density parity-check codes (PBRL codes) are a recently proposed family of easily encodable and decodable rate-compatible LDPC (RC-LDPC) codes. These codes have an excellent iterative decoding threshold and performance across all design rates. PBRL codes designed thus far, for both long and short block-lengths, have been based on optimizing the iterative decoding threshold of the protograph of the RC code family at various design rates. In this work, we propose a design method to obtain better quasi-cyclic (QC) RC-LDPC codes with PBRL structure for short block-lengths (of a few hundred bits). We achieve this by maximizing an upper bound on the minimum distance of any QC-LDPC code that can be obtained from the protograph of a PBRL ensemble. The obtained codes outperform the original PBRL codes at short block-lengths by significantly improving the error floor behavior at all design rates. Furthermore, we identify a reduction in complexity of the design procedure, facilitated by the general structure of a PBRL ensemble.
Low-Density Parity-Check (LDPC) codes are among the most effective modern error-correcting codes due to their excellent correction performance and highly parallel decoding scheme. Moreover, the nonbinary extension of such codes further increases performance in the short-block regime. In this paper, we review the key elements for the construction of implementation-oriented binary and nonbinary codes. These Quasi-Cyclic LDPC (QC-LDPC) codes additionally feature efficient encoder and decoder implementation frameworks. We then present a versatile algorithm for the construction of both binary and nonbinary QC-LDPC codes that have low encoding complexity and an optimized corresponding graph structure. Our algorithm uses a progressive edge growth algorithm, modified for QC-LDPC graph construction, and then performs an iterative global search for optimized cyclic shift values within the QC-LDPC circulants. Strong error correction performance is achieved by minimizing the number of short cycles, and cycles with low external connectivity, within the code graph. We validate this approach via error rate simulations of a transmission system model featuring an LDPC coder-decoder, digital modulation, and additive white Gaussian noise channels. The obtained numerical results validate the effectiveness of the proposed construction algorithm, with a number of constructed codes exhibiting either similar or superior performance to industry standard binary codes and selected nonbinary codes from the literature.
This paper presents an improvement of a puncturing technique for rate-compatible low density parity check (LDPC) codes originally proposed by Asvadi and Banihashemi. In the original technique, the puncturing bits are selected by progressively reducing the search space according to a certain sequence of criteria. The last criterion is based on the ACE (approximate cycle extrinsic message degree) values of the short cycles present in the Tanner graph of the code. In this paper, we propose to substitute the last criterion with one which is based on the absorbing sets of the code. Simulation results show that this scheme improves the performance compared to the original and some other scheme available in the literature.