New decoding scheme for LDPC codes based on simple product code structure

In this paper, a new decoding scheme for low-density parity-check (LDPC) codes using the concept of simple product code structure is proposed based on combining two independently received soft-decision data for the same codeword. LDPC codes act as horizontal codes of the product codes and simple algebraic codes are used as vertical codes to help decoding of the LDPC codes. The decoding capability of the proposed decoding scheme is defined and analyzed using the paritycheck matrices of vertical codes and especially the combined-decodability is derived for the case of single parity-check (SPC) and Hamming codes being used as vertical codes. It is also shown that the proposed decoding scheme achieves much better error-correcting capability in high signal to noise ratio (SNR) region with low additional decoding complexity, compared with a conventional decoding scheme.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Novel LDPC coding and decoding strategies: design, analysis, and algorithms

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

Detection and Removal of Cycles in LDPC Codes

Information technology, at present has thrived to great aspects and every day more beneficiary of this blessing is being connected to the modern invention and technology. With the swift growth of communication networks, there has been a high demand for efficient and reliable digital transmission and data storage system. LDPC is one of the channel codes for error correcting that have been developed for competent systems that require higher reliability. For low-end devices requiring a limited battery or computational power, low complexity decoders are useful. For LDPC codes, the presence of short cycle in the parity-check matrix lower the decoding threshold making it less efficient. In this research, a method has been developed from an existing algorithm that finds out the exact position of potential bits forming cycle-4 in the parity check matrix that might create decoding failure after transmission in binary erasure channel. Once the short cycles are detected, it can be removed by puncturing method to obtain capacity achieving codes. The code obtained by the method has a threshold 0.42 and rate 0.5, which is asymptotically close to the mother code. Simulations show that for less number of iterations and in the presence of same channel erasure the decoder block error probability close to 10-6 is achievable. As no other additional decoding algorithm is employed, the proposed scheme does not add additional computational complexity to the decoder. Furthermore, as an extension to the method a scheme has been proposed to generate rate-compatible LDPC codes using 0.5 rate regular code with puncturing method varying puncturing fractions. By the proposed method of generating different rate code, same amount of information can be sent with less parity

Physical layer forward error correcetion in DVB-S2 networks.

Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2012.The rapid growth of wireless systems has shown little sign of ceasing, due to increased consumer demand for reliable interactive services. A key component of the development has centered on satellite networks, which allows provision of services in scenarios where terrestrial systems are not viable. The Digital Video Broadcasting-Satellite Second Generation (DVB-S2) standard was developed for use in satellite broadcast applications, the foremost being video broadcasting. Inherent to DVB-S2 is a powerful forward error correction (FEC) module, present in both the Physical and Data Link Layer. Improving the error correcting capability of the FEC is a natural advent in improving the quality of service of the protocol. This is more crucial in real time satellite video broadcast where retransmission of data is not viable, due to high latency. The Physical Layer error correcting capability is implemented in the form of a concatenated BCH-LDPC code. The DVB-S2 standard does not define the decoding structure for the receiver system however many powerful decoding systems have been presented in the literature; the Belief Propagation-Chase concatenated decoder being chief amongst them. The decoder utilizes the concept of soft information transfer between the Chase and Belief Propagation (BP) decoders to provide improved error correcting capability above that of the component decoders. The following dissertation is motivated by the physical layer (PL) FEC scheme, focused on the concatenated Chase-BP decoder. The aim is to generate results based on the BP-Chase decoder in a satellite channel as well as improve the error correcting capability. The BP-Chase decoder has shown to be very powerful however the current literature provides performance results only in AWGN channels. The AWGN channel however is not an accurate representation of a land-mobile satellite (LMS) channel; it does not consider the effect of shadowing, which is prevalent in satellite systems. The development of Markov chain models have allowed for better description of the characteristics of the LMS channel. The outcome being the selection of a Ku band LMS channel model. The selected LMS channel model is composed of 3 states, each generating a different degree of shadowing. The PL system has been simulated using the LMS channel and BP-Chase receiver to provide a more accurate representation of performance of a DVB-S2 network. The effect of shadowing has shown to reduce coding performance by approximately 4dB, measured over several code lengths and decoders, when compared with AWGN performance results. The second body of work aims to improve the error correcting capability of the BP-Chase decoder, concentrating on improving the LDPC decoding module performance. The LDPC system is the basis for the powerful error correcting ability of the concatenated scheme. In attempting to improve the LDPC decoder a reciprocal improvement is expected in the overall decoding performance of the concatenated decoder. There have been several schemes presented which improve BP performance. The BP-Ordered statistics decoder (OSD) was selected through a process of literary review; a novel decoding structure is presented incorporating the BP-OSD decoder into the BP-Chase structure. The result of which is the BP-OSD-Chase decoder. The decoder contains two stages of concatenation; the first stage implements the BPOSD algorithm which decodes the LDPC code and the second stage decodes the BCH code using the Chase algorithm. Simulation results of the novel decoder implementation in the DVBS2 PL show a coding gain of 0.45dB and 0.15dB versus the BP and BP-Chase decoders respectively, across both the AWGN and LMS channel

Códigos binários definidos por matrizes de teste de paridade esparsas algoritmos de descodificação

Tese de Mestrado em Engenharia Electrotécnica e de Computadores especialização em Sistemas de Telecomunicações, apresentada ao Departamento de Engenharia Electrotécnica e de Computadores da Fac. de Ciências e Tecnologia de CoimbraEsta dissertação aborda o estudo de algoritmos iterativos para a descodificação de Códigos Binários Definidos por Matrizes de Teste de Paridade Esparsas, também conhecidos por Low Density Parity-Check Codes (LDPC). São considerados como uma das classes de códigos que melhor desempenho apresentam e que num futuro próximo poderão integrar várias normas de comunicação digital. O desenvolvimento científico deste tema, verificado ao longo da última década, é impressionante. Apresentamos um estudo sobre técnicas de descodificação iterativas baseadas no algoritmo Soma de Produtos (SPA). É feita uma análise comparativa e crítica dos vários algoritmos do ponto de vista do desempenho e da complexidade computacional. São abordadas várias técnicas de simplificação do algoritmo SPA, com particular destaque para o algoritmo Soma Mínima. Finalmente, propomos para o algoritmo SPA uma nova técnica de normalização, cujos resultados obtidos evidenciam uma melhoria significativa do desempenho para códigos LDPC longos.The Iterative Decoding of Low Density Parity-Check Codes (LDPC) is the main subject of this thesis. LDPC are seen as one of most powerful classes of error correcting codes which in a near future will probably be included in new digital data transmission standards. In the last decade, the scientific development of this theme was impressive. The Sum Product Algorithm (SPA) and their simplifications are deeply study, with special attention to Min-Sum algorithm. A critical and comparison analysis of different SPA variants is made from the performance and decoding complexity point of view. Finally, we propose a new normalization technique which significantly improves the performance of SPA for long LDPC codes

Initial Synchronisation in the Multiple-Input Multiple-Output Aided Single- and Multi-Carrier DS-CDMA as well as DS-UWB Downlink

In this thesis, we propose and investigate code acquisition schemes employing both colocated and cooperative Multiple Input/Multiple Output (MIMO) aided Single-Carrier (SC) and Multi-Carrier (MC) Code Division Multiple Access (CDMA) DownLink (DL) schemes. We study their characteristics and performance in terms of both Non-Coherent (NC) and Differentially Coherent (DC) MIMO scenarios. Furthermore, we also propose iterative code acquisition schemes for the Direct Sequence-Ultra WideBand (DS-UWB) DL. There is a paucity of code acquisition techniques designed for transmit diversity aided systems. Moreover, there are no in-depth studies representing the fundamental characteristics of code acquisition schemes employing both co-located and cooperative MIMOs. Hence we investigate both NC and DC code acquisition schemes in the co-located and cooperative MIMO aided SC and MC DS-CDMA DL, when communicating over spatially uncorrelated Rayleigh channels. The issues of NC initial and post-initial acquisition schemes as well as DC schemes are studied as a function of the number of co-located antennas by quantifying the attainable correct detection probability and mean acquisition time performances. The research of DS-UWB systems has recently attracted a significant interest in both the academic and industrial community. In the DS-UWB DL, initial acquisition is required for both coarse timing as well as code phase alignment. Both of these constitute a challenging problem owing to the extremely short chip-duration of UWB systems. This leads to a huge acquisition search space size, which is represented as the product of the number of legitimate code phases in the uncertainty region of the PN code and the number of legitimate signalling pulse positions. Therefore the benefits of the iterative code acquisition schemes are analysed in terms of the achievable correct detection probability and mean acquisition time performances. Hence we significantly reduce the search space size with the aid of a Tanner graph based Message Passing (MP) technique, which is combined with the employment of beneficially selected generator polynomials, multiple receive antennas and appropriately designed multiple-component decoders. Finally, we characterise a range of two-stage iterative acquisition schemes employing iterative MP designed for a multiple receive antenna assisted DS-UWB DL scenario