LDPC code used by the advanced communication standard of the next generation is an error control code. Its error correction ability may approach the Shannon’s theoretical value. With the MP algorithm, it can decode received samples in high speed from transmitter. However, the MP method is suboptimum and optimum solution is not guaranteed. In this thesis, a hybrid decoding method is formed by combing the MP and the A* methods. We first make comparison between the MP and A* method and then show their combined performance. From the results, the coding gain of A* model is higher than that of MP model. The decoding complexity increases exponentially with the codeword length for A* method, but the MP method assumes linear increase. Using the hybrid structure, its coding gain is the same as that of A* method. Moreover, decoding complexity is slightly greater than that of MP one. For codeword length 96 bits and coding rate 1/2 and BER = 10E-5, the hybrid structure outperforms 1.4 dB coding gain than the MP method. This improvement only required 1% received sequences to be sent to A* decoding block. Our newly designed hybrid structure can solve both of the high coding gain and low decoding complexity while it has the ability to yield the optimum solution.
LDPC code used by the advanced communication standard of the next generation is an error control code. Its error correction ability may approach the Shannon’s theoretical value. With the MP algorithm, it can decode received samples in high speed from transmitter. However, the MP method is suboptimum and optimum solution is not guaranteed. In this thesis, a hybrid decoding method is formed by combing the MP and the A* methods. We first make comparison between the MP and A* method and then show their combined performance. From the results, the coding gain of A* model is higher than that of MP model. The decoding complexity increases exponentially with the codeword length for A* method, but the MP method assumes linear increase. Using the hybrid structure, its coding gain is the same as that of A* method. Moreover, decoding complexity is slightly greater than that of MP one. For codeword length 96 bits and coding rate 1/2 and BER = 10E-5, the hybrid structure outperforms 1.4 dB coding gain than the MP method. This improvement only required 1% received sequences to be sent to A* decoding block. Our newly designed hybrid structure can solve both of the high coding gain and low decoding complexity while it has the ability to yield the optimum solution.
Because the message passing (MP) method is suboptimum and optimum solutions are not guaranteed, we present a hybrid decoding method by combing the MP and the A* methods. We first make comparison between the MP and A* method and then show their combined performance. Using the hybrid structure, its decoding gain is the same as that of A* method. Moreover, decoding complexity is slightly greater than that of MP one. For codeword length 96 bits and coding rate 1/2 and BER = 10-5, the hybrid structure outperforms 1.4 dB decoding gain than the MP method. This improvement only required 1% received sequences to be transferred to A* decoding block. Our newly designed hybrid structure can solve both of the high decoding gain and low decoding complexity while it has the ability to yield the optimum solution.
Low-density parity-check (LDPC) codes have been the focus of much research over the past decade thanks to their near Shannon limit performance and to their efficient message- passing (MP) decoding algorithms. However, the error floor phenomenon observed in MP decoding, which manifests itself as an abrupt change in the slope of the error-rate curve, has hindered the adoption of LDPC codes and MP decoders in some applications requiring very low error rates. As an alternative to MP decoding, linear programming (LP) decoding is an approximation to maximum-likelihood decoding by relaxing the optimal decoding problem into a linear optimization problem. It has been noticed that, when the symbols error probability in channel output is low, LP decoding has superior error correction performance. However, due to the inefficiency of general- purpose LP solvers which are not optimized for solving LP problems, LP decoding is computationally more complex than MP decoding, especially for codes of large block size. In this dissertation, we first design an efficient exhaustive search algorithm to find all small error-prone substructures, some of which are commonly blamed for certain decoding failures of MP decoding. Then, we investigate the cause of error floors in LDPC codes from the perspective of the MP decoder implementation, with special attention to limitations that decrease the numerical accuracy of messages passed during decoding, and propose a quantization method for fixed-point implementation of MP decoding which significantly improves the error-floor performance by overcoming the limitations of standard quantization rules. For LP decoding, we improve the error-correcting capability of LP decoding by using an effective algorithm to generate additional redundant parity-check constraints which eliminate certain undesired solutions to LP decoding problem. We further propose an efficient message-passing algorithm to solve the LP decoding problem. This algorithm is based on the alternating direction method of multipliers (ADMM), a classic technique in convex optimization theory, and our key contribution is a novel, efficient projection algorithm that can improve the decoding speed of the ADMM- based LP decoder. The last part of this dissertation is a separate piece of work on optimizing video transmission over distributed cognitive radio network
Channel coding technique is a fundamental building block in any modern communication system to realize reliable, fast, and secure data transmission. At the same time, it is a challenging and crucial task, as the data transmission happens in a channel where noise, fading, and other impairments are present. The Low-Density Parity-Check (LDPC) codes give substantial results close to the Shannon limit when the complexity and processing delay time are unlimited. In this paper, the performance of the LDPC decoding with four algorithms was investigated. The investigated four algorithms were Belief Propagation (BP), Layered Belief Propagation (LBP), Normalized min-sum (NMS), and Offset min-sum (OMS). These algorithms were examined for code rates ranging from 1/3 to 9/10 and message block lengths (64, 512, 1024, and 5120) bits. The simulation results revealed the flexibility of these decoders in supporting these code rates and block lengths, which enables their usage in a wide range of applications and scenarios for fifth-generation (5G) wireless communication. In addition, the effect of the maximum number of decoding iterations on the error correction performance was investigated, and a gain of 5.6 dB can be obtained by using 32 decoding iterations at BER=2*10-3 instead of one decoding iteration. The results showed that the decoders performed better for longer message blocks than for short message blocks, and less power was required for transmitting longer messages. Finally, the comparison results of their performance in terms of bit error rate (BER) under the same conditions showed a gain of 0.8 dB using LBP at BER= 10-5 compared with the NMS decoding algorithm.
In this paper, an iterative soft-decision hybrid decoding algorithm for non-binary low-density parity-check (LDPC) codes with short codeword lengths is proposed. The rationale of the approach is to combine the classical belief propagation (BP) iterative LDPC decoding algorithm with the most reliable basis (MRB) decoding algorithm. This allows to achieve significant performance improvements, with a complexity that, for medium/low error rates, is only slightly higher than that of the BP algorithm alone. The performance improvement with respect to pure BP decoding is up to 0.7 dB at codeword error rate (CER) ≈ 10-5. Notably, for a fixed MRB order, hybrid decoding achieves a gain up to 0.5 dB at CER ≈ 10-5with respect to BP decoding and MRB decoding used alone.
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.