Author: Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Design and Implementation for Non-binary Low-density Parity-check Codes (NB-LDPC) Decoders
High-Performance and Energy-Efficient Decoder Design for Non-Binary LDPC Codes
Author: Yuta ToriyamaPublisher:
ISBN:
Category :
Languages : en
Pages : 133
Book Description
Binary Low-Density Parity-Check (LDPC) codes are a type of error correction code known to exhibit excellent error-correcting capabilities, and have increasingly been applied as the forward error correction solution in a multitude of systems and standards, such as wireless communications, wireline communications, and data storage systems. In the pursuit of codes with even higher coding gain, non-binary LDPC (NB-LDPC) codes defined over a Galois field of order q have risen as a strong replacement candidate. For codes defined with similar rate and length, NB-LDPC codes exhibit a significant coding gain improvement relative to that of their binary counterparts. Unfortunately, NB-LDPC codes are currently limited from practical application by the immense complexity of their decoding algorithms, because the improved error-rate performance of higher field orders comes at the cost of increasing decoding algorithm complexity. Currently available ASIC implementation solutions for NB-LDPC code decoders are simultaneously low in throughput and power-hungry, leading to a low energy efficiency. We propose several techniques at the algorithm level as well as hardware architecture level in an attempt to bring NB-LDPC codes closer to practical deployment. On the algorithm side, we propose several algorithmic modifications and analyze the corresponding hardware cost alleviation as well as impact on coding gain. We also study the quantization scheme for NB-LDPC decoders, again in the context of both the hardware and coding gain impacts, and we propose a technique that enables a good tradeoff in this space. On the hardware side, we develop a FPGA-based NB-LDPC decoder platform for architecture prototyping as well as hardware acceleration of code evaluation via error rate simulations. We also discuss the architectural techniques and innovations corresponding to our proposed algorithm for optimization of the implementation. Finally, a proof-of-concept ASIC chip is realized that integrates many of the proposed techniques. We are able to achieve a 3.7x improvement in the information throughput and 23.8x improvement in the energy efficiency over prior state-of-the-art, without sacrificing the strong error correcting capabilities of the NB-LDPC code.
Efficient VLSI Architectures for Non-binary Low Density Parity Check Decoding
Author: Fang CaiPublisher:
ISBN:
Category :
Languages : en
Pages : 95
Book Description
Non-binary low-density parity-check (NB-LDPC) codes can achieve better error-correcting performance than binary LDPC codes when the code length is moderate at the cost of higher decoding complexity. The high complexity is mainly caused by the complicated computations in the check node processing and the large memory requirement. In this thesis, two VLSI designs for NB-LDPC decoders based on two novel check node processing schemes are proposed. The first design is based on forward-backward check node processing. A novel scheme and corresponding architecture are developed to implement the elementary step of the check node processing. In our design, layered decoding is applied and only nm less than q messages are kept on each edge of the associated Tanner graph. The computation units and the scheduling of the computations are optimized in the context of layered decoding to reduce the area requirement and increase the speed. This thesis also introduces an overlapped method for the check node processing among different layers to further speed up the decoding. From complexity and latency analysis, our design is much more efficient than any previous design. Our proposed decoder for a (744, 653) code over GF(32) has also been synthesized on a Xilinx Virtex-2 Pro FPGA device. It can achieve a throughput of 9.30 Mbps when 15 decoding iterations are carried out. The second design is based on a proposed trellis based check node processing scheme. The proposed scheme first sorts out a limited number of the most reliable variable-to-check (v-to-c) messages, then the check-to-variable (c-to-v) messages to all connected variable nodes are derived independently from the sorted messages without noticeable performance loss. Compared to the previous iterative forward-backward check node processing, the proposed scheme not only significantly reduced the computation complexity, but eliminated the memory required for storing the intermediate messages generated from the forward and backward processes. Inspired by this novel c-to-v message computation method, we propose to store the most reliable v-to-c messages as 'compressed' c-to-v messages. The c-to-v messages will be recovered from the compressed format when needed. Accordingly, the memory requirement of the overall decoder can be substantially reduced. Compared to the previous Min-max decoder architecture, the proposed design for a (837, 726) code over GF(32) can achieve the same throughput with only 46% of the area.
Low-complexity Decoding Algorithms and Architectures for Non-binary LDPC Codes
Author: Fang CaiPublisher:
ISBN:
Category :
Languages : en
Pages : 149
Book Description
Non-binary low-density parity-check (NB-LDPC) codes can achieve better error-correcting performance than their binary counterparts when the code length is moderate at the cost of higher decoding complexity. The high complexity is mainly caused by the complicated computations in the check node processing and the large memory requirement. In this thesis, three decoding algorithms and corresponding VLSI architectures are proposed for NB-LDPC codes to lower the computational complexity and memory requirement. The first design is based on the proposed relaxed Min-max decoding algorithm. A novel relaxed check node processing scheme is proposed for the Min-max NB-LDPC decoding algorithm. Each finite field element of GF(2p̂) can be uniquely represented by a linear combination of $p$ independent field elements. Making use of this property, an innovative method is developed in this paper to first find a set of the p most reliable variable-to-check messages with independent field elements, called the minimum basis. Then the check-to-variable messages are efficiently computed from the minimum basis. With very small performance loss, the complexity of the check node processing can be substantially reduced using the proposed scheme. In addition, efficient VLSI architectures are developed to implement the proposed check node processing and overall NB-LDPC decoder. Compared to the most efficient prior design, the proposed decoder for a (837, 726) NB-LDPC code over GF(25̂) can achieve 52% higher efficiency in terms of throughput-over-area ratio. The second design is based on a proposed enhanced iterative hard reliability-based majority-logic decoding. The recently developed iterative hard reliability-based majority-logic NB-LDPC decoding has better performance-complexity tradeoffs than previous algorithms. Novel schemes are proposed for the iterative hard reliability-based majority-logic decoding (IHRB-MLGD). Compared to the IHRB algorithm, our enhanced (E- )IHRB algorithm can achieve significant coding gain with small hardware overhead. Then low-complexity partial-parallel NB-LDPC decoder architectures are developed based on these two algorithms. Many existing NB-LDPC code construction methods lead to quasi-cyclic or cyclic codes. Both types of codes are considered in our design. Moreover, novel schemes are developed to keep a small proportion of messages in order to reduce the memory requirement without causing noticeable performance loss. In addition, a shift-message structure is proposed by using memories concatenated with variable node units to enable efficient partial-parallel decoding for cyclic NB-LDPC codes. Compared to previous designs based on the Min-max decoding algorithm, our proposed decoders have at least tens of times lower complexity with moderate coding gain loss. The third design is based on a proposed check node decoding scheme using power representation of finite field elements. Novel schemes are proposed for the Min-max check node processing by making use of the cyclical-shift property of the power representation of finite field elements. Compared to previous designs based on the Min-max algorithm with forward-backward scheme, the proposed check node units (CNUs) do not need the complex switching network. Moreover, the multiplications of the parity check matrix entries are efficiently incorporated. For a Min-max NB-LDPC decoder over GF(32), the proposed scheme reduces the CNU area by at least 32%, and leads to higher clock frequency.
Decoder Architectures and Implementations for Quasi-cyclic Low-density Parity-check Codes
Author: Xiaoheng ChenPublisher:
ISBN: 9781124906669
Category :
Languages : en
Pages :
Book Description
Since the rediscovery of low-density parity-check (LDPC) codes in the late 1990s, tremendous progress has been made in code construction and design, decoding algorithms, and decoder implementation of these capacity-approaching codes. Recently, LDPC codes are considered for applications such as high-speed satellite and optical communications, the hard disk drives, and high-density flash memory based storage systems, which require that the codes are free of error-floor down to bit error rate (BER) as low as 10−12 to 10−15. FPGAs are usually used to evaluate the error performance of codes, since one can exploit the finite word length and extremely high internal memory bandwidth of an FPGA. Existing FPGA-based LDPC decoders fail to utilize the configurability and read-first mode of embedded memory in the FPGAs, and thus result in limited throughput and codes sizes. Four optimization techniques, i.e., vectorization, folding, message relocation, and circulant permutation matrix (CPM) sharing, are proposed to improve the throughput, scalability, and efficiency of FPGA-based decoders. Also, a semi-automatic CAD tool called QCSYN (Quasi-Cyclic LDPC decoder SYNthesis) is designed to shorten the implementation time of decoders. Using the above techniques, a high-rate (16129,15372) code is shown to have no error-floor down to the BER of 10−14. Also, it is very difficult to construct codes that do not exhibit an error floor down to 10−15 or so. Without detailed knowledge of dominant trapping sets, a backtracking-based reconfigurable decoder is designed to lower the error floor of a family of structurally compatible quasi-cyclic LDPC codes by one to two orders of magnitudes. Hardware reconfigurability is another significant feature of LDPC decoders. A tri-mode decoder for the (4095,3367) Euclidean geometry code is designed to work with three compatible binary message passing decoding algorithms. Note that this code contains 262080 edges (21.3 times of the (2048,1723) 10GBASE-T code) in its Tanner graph and is the largest code ever implemented. Besides, an efficient QC-LDPC Shift Network (QSN) is proposed to reduce the interconnect delay and control logic of circular shift network, a core component in the reconfigurable decoder that supports a family of structurally compatible codes. The interconnect delay and control logic area are reduced by a factor of 2.12 and 8, respectively. Non-binary LDPC codes are effective in combating burst errors. Using the power representation of the elements in the Galois field to organize both intrinsic and extrinsic messages, we present an efficient decoder architecture for non-binary QC-LDPC codes. The proposed decoder is reconfigurable and can be used to decode any code of a given field size. The decoder supports both regular and irregular non-binary QC-LDPC codes. Using a practical metric of throughput per unit area, the proposed implementation outperforms the best implementations published in research literature to date.
Implementation Aspects of Binary and Non-binary Low-density Parity-check Decoders
Author: Philipp SchläferPublisher:
ISBN: 9783959740531
Category :
Languages : en
Pages :
Book Description
LDPC Code Designs, Constructions, and Unification
Author: Juane LiPublisher: Cambridge University Press
ISBN: 131681310X
Category : Technology & Engineering
Languages : en
Pages : 259
Book Description
Written by leading experts, this self-contained text provides systematic coverage of LDPC codes and their construction techniques, unifying both algebraic- and graph-based approaches into a single theoretical framework (the superposition construction). An algebraic method for constructing protograph LDPC codes is described, and entirely new codes and techniques are presented. These include a new class of LDPC codes with doubly quasi-cyclic structure, as well as algebraic methods for constructing spatially and globally coupled LDPC codes. Authoritative, yet written using accessible language, this text is essential reading for electrical engineers, computer scientists and mathematicians working in communications and information theory.
Non-Binary Error Control Coding for Wireless Communication and Data Storage
Author: Rolando Antonio CarrascoPublisher: John Wiley & Sons
ISBN: 047074040X
Category : Technology & Engineering
Languages : en
Pages : 322
Book Description
Comprehensive introduction to non-binary error-correction coding techniques Non-Binary Error Control Coding for Wireless Communication and Data Storage explores non-binary coding schemes that have been developed to provide an alternative to the Reed – Solomon codes, which are expected to become unsuitable for use in future data storage and communication devices as the demand for higher data rates increases. This book will look at the other significant non-binary coding schemes, including non-binary block and ring trellis-coded modulation (TCM) codes that perform well in fading conditions without any expansion in bandwidth use, and algebraic-geometric codes which are an extension of Reed-Solomon codes but with better parameters. Key Features: Comprehensive and self-contained reference to non-binary error control coding starting from binary codes and progressing up to the latest non-binary codes Explains the design and construction of good non-binary codes with descriptions of efficient non-binary decoding algorithms with applications for wireless communication and high-density data storage Discusses the application to specific cellular and wireless channels, and also magnetic storage channels that model the reading of data from the magnetic disc of a hard drive. Includes detailed worked examples for each coding scheme to supplement the concepts described in this book Focuses on the encoding, decoding and performance of both block and convolutional non-binary codes, and covers the Kötter-Vardy algorithm and Non-binary LDPC codes This book will be an excellent reference for researchers in the wireless communication and data storage communities, as well as development/research engineers in telecoms and storage companies. Postgraduate students in these fields will also find this book of interest.
Analysis, Design and Application of Nonbinary Low-density Parity Check Codes
Author: Ge LiError Control Coding for B3G/4G Wireless Systems
Author: Thierry LestablePublisher: John Wiley & Sons
ISBN: 0470977590
Category : Technology & Engineering
Languages : en
Pages : 263
Book Description
Covering the fast evolving area of advanced coding, Error Control Coding for B3G/4G Wireless Systems targets IMT-Advanced systems to present the latest findings and implementation solutions. The book begins by detailing the fundamentals of advanced coding techniques such as Coding, Decoding, Design, and Optimization. It provides not only state-of-the-art research findings in 3D Turbo-codes, non-binary LDPC Codes, Fountain, and Raptor codes, but also insights into their real-world implementation by examining hardware architecture solutions, for example VLSI complexity, FPGA, and ASIC. Furthermore, special attention is paid to Incremental redundancy techniques, which constitute a key feature of Wireless Systems. A promising application of these advanced coding techniques, the Turbo-principle (also known as iterative processing), is illustrated through an in-depth discussion of Turbo-MIMO, Turbo-Equalization, and Turbo-Interleaving techniques. Finally, the book presents the status of major standardization activities currently implementing such techniques, with special interest in 3GPP UMTS, LTE, WiMAX, IEEE 802.11n, DVB-RCS, DVB-S2, and IEEE 802.22. As a result, the book coherently brings together academic and industry vision by providing readers with a uniquely comprehensive view of the whole topic, whilst also giving an understanding of leading-edge techniques. Includes detailed coverage of coding, decoding, design, and optimization approaches for advanced codes Provides up to date research findings from both highly reputed academics and industry standpoints Presents the latest status of standardization activities for Wireless Systems related to advanced coding Describes real-world implementation aspects by giving insights into architecture solutions for both LDPC and Turbo-codes Examines the most advanced and promising concepts of turbo-processing applications: Turbo-MIMO, Turbo-Equalization, Turbo-Interleaving