Download or read book VLSI Architectures For Soft Decision Decoding Of Reed Solomon Codes written by Jiangli Zhu and published by LAP Lambert Academic Publishing. This book was released on 2012 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Error-correcting coding has become one integral part in nearly all the modern data transmission and storage systems. Due to the powerful error-correcting capability, Reed-Solomon (RS) codes are among the most extensively used error-correcting codes with applications in wireless communications, deep-space probing, magnetic and optical recording, and digital television. Traditional hard-decision decoding (HDD) algorithms of RS codes can correct as many symbol errors as half the minimum distance of the code. Recently, much attention has been paid to algebraic soft-decision decoding (ASD) algorithms of RS codes. These algorithms incorporate channel probabilities into an algebraic interpolation process. As a result, significant coding gain can be achieved with a complexity that is polynomial in codeword length. Practical ASD algorithms include the Koetter-Vardy, low-complexity Chase (LCC) and bit-level generalized minimum distance (BGMD) decodings. This book focuses on the design of efficient VLSI architectures for ASD decoders.

Download or read book Efficient VLSI Architectures for Algebraic Soft decision Decoding of Reed Solomon Codes written by Jiangli Zhu and published by . This book was released on 2011 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic soft-decision decoding (ASD) algorithms of Reed-Solomon (RS) codes have attracted much interest due to their significant coding gain and polynomial complexity. Practical ASD algorithms include the Koetter-Vardy, low-complexity Chase (LCC) and bit-level generalized minimum distance (BGMD) decodings. This thesis focuses on the design of efficient VLSI architectures for ASD decoders. One major step of ASD algorithms is the interpolation. Available interpolation algorithms can only add interpolation points or increase interpolation multiplicities. However, backward interpolation, which eliminates interpolation points or reduces multiplicities, is indispensable to enable the re-using of interpolation results. In this thesis, a novel backward interpolation is first proposed for the LCC decoding through constructing equivalent Grbner bases. In the LCC decoding, 2 test vectors need to be interpolated over. With backward interpolation, the interpolation result for each of the second and later test vectors can be computed by only one backward and one forward interpolation iterations. Compared to the previous design, the proposed backward-forward interpolation scheme can lead to significant memory saving. To reduce the interpolation latency of the LCC decoding, a unified backward-forward interpolation is proposed to carry out both interpolations in a single iteration. With only 40percent area overhead, the proposed unified interpolation architecture can almost double the throughput when large is adopted. Moreover, a reduced-complexity multi-interpolator scheme is developed for the low-latency LCC decoding. The proposed backward interpolation is further extended to the iterative BGMD decoding. By reusing the interpolation results, at least 40 percent of the interpolation iterations can be saved for a (255, 239) code while the area overhead is small. Further speedup of the BGMD interpolation is limited by the inherent serial nature of the interpolation algorithm. In this thesis, a novel interpolation scheme that can combine multiple interpolation iterations is developed. Efficient architectures are presented to integrate the combined and backward interpolation techniques. A combined-backward interpolator of a (255, 239) code is implemented and can achieve a throughput of 440 Mbps on a Xilinx XC2V4000 FPGA device. Compared to the previous fastest implementation, our implementation can achieve a speedup of 64percent with 51percent less FPGA resource. The factorization is another major step of ASD algorithms. In the re-encoded LCC decoding, it is proved that the factorization step can be eliminated. Hence, the LCC decoder can be further simplified. In the reencoded ASD decoders, a re-encoder and an erasure decoder need to be added. These two blocks can take a significant proportion of the overall decoder area and may limit the achievable throughput. An efficient re-encoder design is proposed by computing the erasure locator and evaluator through direct multiplications and reformulating other involved computations. When applied to a (255, 239) code, our re-encoder can achieve 82percent higher throughput than the previous design with 11percent less area. With minor modifications, the proposed design can also be used to implement erasure decoder. After applying available complexity-reducing techniques, complexity comparisons for three practical ASD decoders were carried out. It is derived that the LCC decoder can achieve similar or higher coding gain with lower complexity for high-rate codes. This thesis also provides discussions on how the hardware complexities of ASD decoders change with codeword length, code rate and other parameters.

Download or read book Efficient Algebraic Soft decision Decoding of Reed Solomon Codes written by Jun Ma and published by . This book was released on 2007 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: A divide-and-conquer approach to perform the bivariate polynomial interpolation procedure is discussed in Chapter 3. This method can potentially reduce the interpolation complexity of algebraic soft-decision decoding of Reed-Solomon code.

Download or read book VLSI Architectures for Modern Error Correcting Codes written by Xinmiao Zhang and published by CRC Press. This book was released on 2017-12-19 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Error-correcting codes are ubiquitous. They are adopted in almost every modern digital communication and storage system, such as wireless communications, optical communications, Flash memories, computer hard drives, sensor networks, and deep-space probing. New-generation and emerging applications demand codes with better error-correcting capability. On the other hand, the design and implementation of those high-gain error-correcting codes pose many challenges. They usually involve complex mathematical computations, and mapping them directly to hardware often leads to very high complexity. VLSI Architectures for Modern Error-Correcting Codes serves as a bridge connecting advancements in coding theory to practical hardware implementations. Instead of focusing on circuit-level design techniques, the book highlights integrated algorithmic and architectural transformations that lead to great improvements on throughput, silicon area requirement, and/or power consumption in the hardware implementation. The goal of this book is to provide a comprehensive and systematic review of available techniques and architectures, so that they can be easily followed by system and hardware designers to develop en/decoder implementations that meet error-correcting performance and cost requirements. This book can be also used as a reference for graduate-level courses on VLSI design and error-correcting coding. Particular emphases are placed on hard- and soft-decision Reed-Solomon (RS) and Bose-Chaudhuri-Hocquenghem (BCH) codes, and binary and non-binary low-density parity-check (LDPC) codes. These codes are among the best candidates for modern and emerging applications due to their good error-correcting performance and lower implementation complexity compared to other codes. To help explain the computations and en/decoder architectures, many examples and case studies are included. More importantly, discussions are provided on the advantages and drawbacks of different implementation approaches and architectures.

Download or read book High speed VLSI Architectures for Error correcting Codes and Cryptosystems written by Xinmiao Zhang and published by . This book was released on 2005 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Fundamentals of Classical and Modern Error Correcting Codes written by Shu Lin and published by Cambridge University Press. This book was released on 2021-12-09 with total page 843 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible textbook that uses step-by-step explanations, relatively easy mathematics and numerous examples to aid student understanding.

Download or read book High Speed and Low Power VLSI Error Control Coders written by and published by . This book was released on 2004 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: This final report describes our research results obtained during the period August 1, 2001 to July 31, 2004 by support from the ARO grant "High Speed and Low Power VLSI Error Control Coders" (ARO Grant Number:DA/DAAD19-01-1-0705(42436-CI). Research results obtained in the areas of architectures for product turbo coders (based on component codes such as BCH codes, extended Hamming codes, and single parity check codes), space-time block codes, low-density parity check (LDPC) and long BCH codes are described. Efficient implementation of AES cryptosystems are described. Architectures for ultra wideband communication systems are summarized. Erasure decoding in Reed-Solomon codes and some preliminary results on soft-decision Reed-Solomon decoders are outlined.

Download or read book Efficient Soft decision Decoding of Reed Solomon Codes written by Cheng Zhong and published by . This book was released on 2008 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Soft decision Decoding of Reed Solomon Codes Using Pattern Information Over Partial Response Channels written by Soowoong Lee and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Aspects in Soft Decision Decoding of Reed solomon Codes written by Uri Assaf and published by . This book was released on 2004 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book High Speed and Low Complexity Architecture Designs for Hard Decision Soft Decision Reed Solomon Decoding written by 陸永馗 and published by . This book was released on 2012 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Low Complexity Bit Level Soft decision Decoding for Reed Solomon Codes written by Min-seok Oh and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Soft Decision Decoding for Reed Solomon Codes and Applications written by Edelmar Urba and published by . This book was released on 1999 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Advanced Hardware Design for Error Correcting Codes written by Cyrille Chavet and published by Springer. This book was released on 2014-10-30 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides thorough coverage of error correcting techniques. It includes essential basic concepts and the latest advances on key topics in design, implementation, and optimization of hardware/software systems for error correction. The book’s chapters are written by internationally recognized experts in this field. Topics include evolution of error correction techniques, industrial user needs, architectures, and design approaches for the most advanced error correcting codes (Polar Codes, Non-Binary LDPC, Product Codes, etc). This book provides access to recent results, and is suitable for graduate students and researchers of mathematics, computer science, and engineering. • Examines how to optimize the architecture of hardware design for error correcting codes; • Presents error correction codes from theory to optimized architecture for the current and the next generation standards; • Provides coverage of industrial user needs advanced error correcting techniques. Advanced Hardware Design for Error Correcting Codes includes a foreword by Claude Berrou.

Download or read book On the Performance of Algebraic Soft Decision Decoding Algorithm of Reed Solomon Codes written by Niranjan Nayak Ratnakar and published by . This book was released on 2003 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Algebraic Soft decision Decoding Techniques for High density Magnetic Recording written by Michael Kuei-Che Cheng and published by . This book was released on 2004 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book VLSI Architectures for Multi Gbps Low Density Parity Check Decoders written by Ahmad Darabiha and published by . This book was released on 2008 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Near-capacity performance and parallelizable decoding algorithms have made Low-Density Parity Check (LDPC) codes a powerful competitor to previous generations of codes, such as Turbo and Reed Solomon codes, for reliable high-speed digital communications. As a result, they have been adopted in several emerging standards. This thesis investigates VLSI architectures for multi-Gbps power and area-efficient LDPC decoders. To reduce the node-to-node communication complexity, a decoding scheme is proposed in which messages are transferred and computed bit-serially. Also, a broadcasting scheme is proposed in which the traditional computations required in the sum-product and min-sum decoding algorithms are repartitioned between the check and variable node units. To increase decoding throughput, a block interlacing scheme is investigated which is particularly advantageous in fully-parallel LDPC decoders. To increase decoder energy efficiency, an efficient early termination scheme is proposed. In addition, an analysis is given of how increased hardware parallelism coupled with a reduced supply voltage is a particularly effective approach to reduce the power consumption of LDPC decoders. These architectures and circuits are demonstrated in two hardware implementations. Specifically, a 610-Mbps bit-serial fully-parallel (480, 355) LDPC decoder on a single Altera Stratix EP1S80 device is presented. To our knowledge, this is the fastest FPGA-based LDPC decoder reported in the literature. A fabricated 0.13-mum CMOS bit-serial (660, 484) LDPC decoder is also presented. The decoder has a 300 MHz maximum clock frequency and a 3.3 Gbps throughput with a nominal 1.2-V supply and performs within 3 dB of the Shannon limit at a BER of 10-5. With more than 60% power saving gained by early termination, the decoder consumes 10.4 pJ/bit/iteration at Eb=N0=4dB. Coupling early termination with supply voltage scaling results in an even lower energy consumption of 2.7 pJ/bit/iteration with 648 Mbps decoding throughput. The proposed techniques demonstrate that the bit-serial fully-parallel architecture is preferred to memory-based partially-parallel architectures, both in terms of throughput and energy efficiency, for applications such as 10GBase-T which use medium-size LDPC code (e.g., 2048 bit) and require multi-Gbps decoding throughput.