Stochastic List Decoding of High-Density Parity-Check Codes PDF Download
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Languages : en
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Author: Saeed Sharifi Tehrani
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Languages : en
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Author: Kuo-Lun Huang
Publisher:
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Category : Algorithms
Languages : en
Pages : 125
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The expanding demand for high-speed communications has resulted in development of high-throughput error-correcting techniques required by emerging communication standards. Low-Density Parity-Check (LDPC) codes are a class of linear block codes that achieve near-capacity performance and have been selected as part of many digital communication standards. Stochastic computation has been proposed as a hardware efficient approach for decoding LDPC codes. Using stochastic computation, all messages in the iterative decoding process are represented by Bernoulli sequences. Computations on these sequences are performed bit-by-bit using simple logic operations. Furthermore, serial messages used in stochastic decoders help alleviate routing congestion in hardware implementation of decoder. These factors make stochastic decoding a low complexity alternative to implement LDPC decoders. In this dissertation, we analyze the characteristics of stochastic decoding and propose reduced-latency designs for stochastic LDPC decoders to achieve improved performance on various channel models. We statistically analyze the behavior of stochastic LDPC decoding, including randomization in the stochastic streams and convergence of transition probabilities in iterative decoding process. We also present a space and time-efficient code bit determination method for stochastic LDPC decoders. In addition, we investigate and characterize the decoding errors of stochastic LDPC decoders and as an example, study the stochastic-decoding-specific trapping sets in the (1056,528) LDPC code used in the WiMAX standard. This study helps to develop methods to lower the error floor of stochastic decoding. We propose a reduced-latency stochastic decoding algorithm for LDPC codes. The proposed algorithm, called Conditional Stochastic Decoding (CSD), improves error rate performance and reduces the decoding latency by more than 30% compared with the existing stochastic decoders. We also characterize the performance of CSD in various communication schemes. For example, we show the advantages of using the proposed CSD algorithm in the Automatic Repeat reQuest (ARQ) scheme when compared with other iterative decoding algorithms. We extend our study of stochastic decoding to non-AWGN channel models including the Binary Symmetric Channel (BSC), the Z-channel, and the Rayleigh fading channel. We introduce scaling methods to improve the performance of stochastic decoding on these channel models. On the Rayleigh fading channel, the proposed method not only reduces the computational complexity of the stochastic decoding, but also provides 3-dB improvement in performance and lowers the error floor. Simplicity of hardware implementation, low latency, and good error rate performance of the proposed schemes make them suitable for emerging communication standards.
Author: Assem Shoukry Mohamed Hussein
Publisher:
ISBN:
Category : Decoders (Electronics)
Languages : en
Pages : 66
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Low-density Parity-check (LDPC) codes are very powerful linear error-correcting codes, first introduced by Gallager in 1963. They are now used in many communication standards due to their ability to achieve near Shannon-capacity performance. Stochastic decoding is a hardware-efficient method of iterative decoding of LDPC codes. In this work, we investigate the capability of stochastic decoding to tolerate circuit soft errors while maintaining good bit error rate performance and low error floor. Soft errors can be intended faults as a result of either supply voltage scaling to reduce power consumption or overclocking the system to achieve a higher throughput. They can also be unintended faults as a result of temperature or process variations. We develop two models to emulate these circuit errors at the system level. We apply our models to two standardized LDPC codes (10GBASE-T and WiMAX). Simulation results show that stochastic decoding is very tolerant to faults and errors, where it can tolerate a probability of setup time violation of 0.1 in the wires of the decoder. Hence, stochastic decoding can be very useful in systems with very low power or high performance requirements where we can push the limits of power or speed by lowering the supply voltage or highly overclocking the system while maintaining good performance. In addition, a chip has been designed and sent to fabrication to do post-silicon validation and verify our models.
Author: Vikram Arkalgud Chandrasetty
Publisher: Academic Press
ISBN: 0128112565
Category : Technology & Engineering
Languages : en
Pages : 192
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This book takes a practical hands-on approach to developing low complexity algorithms and transforming them into working hardware. It follows a complete design approach – from algorithms to hardware architectures - and addresses some of the challenges associated with their design, providing insight into implementing innovative architectures based on low complexity algorithms.The reader will learn: Modern techniques to design, model and analyze low complexity LDPC algorithms as well as their hardware implementation How to reduce computational complexity and power consumption using computer aided design techniques All aspects of the design spectrum from algorithms to hardware implementation and performance trade-offs Provides extensive treatment of LDPC decoding algorithms and hardware implementations Gives a systematic guidance, giving a basic understanding of LDPC codes and decoding algorithms and providing practical skills in implementing efficient LDPC decoders in hardware Companion website containing C-Programs and MATLAB models for simulating the algorithms, and Verilog HDL codes for hardware modeling and synthesis
Author: Weiqiang Liu
Publisher: Springer Nature
ISBN: 3030983471
Category : Technology & Engineering
Languages : en
Pages : 607
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Book Description
This book explores the technological developments at various levels of abstraction, of the new paradigm of approximate computing. The authors describe in a single-source the state-of-the-art, covering the entire spectrum of research activities in approximate computing, bridging device, circuit, architecture, and system levels. Content includes tutorials, reviews and surveys of current theoretical/experimental results, design methodologies and applications developed in approximate computing for a wide scope of readership and specialists. Serves as a single-source reference to state-of-the-art of approximate computing; Covers broad range of topics, from circuits to applications; Includes contributions by leading researchers, from academia and industry.
Author: Venkatesan Guruswami
Publisher: Now Publishers Inc
ISBN: 1601980043
Category : Computers
Languages : en
Pages : 110
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Algorithmic Results in List Decoding introduces and motivates the problem of list decoding, and discusses the central algorithmic results of the subject, culminating with the recent results on achieving "list decoding capacity." The main technical focus is on giving a complete presentation of the recent algebraic results achieving list decoding capacity, while pointers or brief descriptions are provided for other works on list decoding. Algorithmic Results in List Decoding is intended for scholars and graduate students in the fields of theoretical computer science and information theory. The author concludes by posing some interesting open questions and suggests directions for future work.
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Publisher: World Scientific
ISBN:
Category :
Languages : en
Pages : 1131
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Author: Shashwat Silas
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Category :
Languages : en
Pages :
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Completely random codes, random linear codes and Gallager's Low Density Parity Check (LDPC) codes are amongst the most fundamental and well-studied error correcting codes. A complete understanding of the combinatorial properties of completely random and random linear codes is important for informing our basic beliefs about what properties any error correcting code can achieve. As such, these questions have received great attention since the very conception of the field. LDPC codes are uniquely important in error-correction due to their vast practical use and fast decoding algorithms. However, precious little had been understood about their combinatorial properties beyond a proof that they achieve the Gilbert-Varshamov bound over binary alphabets, which was provided by Gallager in the 1960s. We develop a new method to precisely characterize vast groups of combinatorial properties for completely random and random linear codes. These groups of properties are general enough to include many of coding theory's most popular obsessions like distance, list-decoding, list-recovery, and their meaningful variants. Our main conceptual contributions are the characterization theorems for symmetric properties of random codes and local properties of random linear codes. In these results, we show that for any property under consideration, there is a 'threshold rate' associated to the property: below that rate it is highly unlikely for the code to achieve the property, and even slightly above that rate it is almost certain. Further, we also give a simple characterization for this threshold rate. In our view, the discovery and characterization of such 'phase transitions' for large classes of natural properties of these error correcting codes is fundamental. Further, it ties in neatly with a line of highly influential work in graph theory and boolean functions (which describes similar phenomena in those domains) beginning with Erdos in the 1950s. Finally, we show that if a random linear code achieves a local property, then so does an LDPC code the same rate. We use our characterizations to show a variety of new results about properties of completely random and random linear codes which are of particular interest to coding theorists. For random linear codes, perhaps our most compelling result shows that the list size of a binary random linear code takes just one of three values with all but negligible probability. Since completely random codes are considered quite 'easy' to analyze, an informed reader may be surprised that there are meaningful questions yet to be answered in this domain. Even here, our techniques give several new results. Notably, we can precisely compute the threshold rate for completely random codes to achieve properties such as perfect hashing and list-of-two decodability. Most surprisingly perhaps, we show that for a large class of combinatorial properties, Gallager's LDPC codes are as good as random linear codes. We hope that this particular result opens new paths towards solving the central open problems in coding theory: (i) finding explicit constructions of binary codes which achieve the GV bound and list-decoding capacity, (ii) finding linear time algorithms for list-decoding codes up to capacity.
Author: Weili Wu
Publisher: Springer Nature
ISBN: 3031491939
Category : Computers
Languages : en
Pages : 430
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Book Description
This two volume set volume LNCS 14422-14423 constitutes the refereed proceedings of the 29th International Conference, COCOON 2023, held in Hawaii, HI, USA, during December 2023. The 60 full papers were carefully reviewed and selected from 146 submissions. They are organized in the following topical sections: Part I : Combinatorics and Algorithms; Algorithmic Solution in Applications; and Algorithm in Networks. Part II: Complexity and Approximation; Graph Algorithms; and Applied Algorithms.
