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Author: Harsh Aurora
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
"Error correcting codes are essential in realizing reliable communication over noisy channels. Polar codes are a recent class of linear block error correcting codes, and are the first of their kind to have an explicit construction and asymptotically achieve the symmetric channel capacity over binary-input discrete memoryless channels. They have recently been adopted into the 5G standard in the eMBB control channel. The successive cancellation list decoding algorithm yields near-optimal decoding performance at the cost of high implementation complexity. The successive cancellation stack algorithm has been shown to provide similar decoding performance at a much lower computational complexity, but suffers from a large memory requirement that scales quadratically with the code length, rendering it impractical in most applications. This thesis presents several approaches to increase the practicality of the successive cancellation stack decoding algorithm in software implementations. First, multiple copies of decoder memory are replaced with a single memory, and the stack sorting step is replaced by a linear search. While this comes at the cost of an increase in computational complexity, results show that the large memory requirement and sorting are amongst primary culprits in the mediocre throughput performance of the software stack algorithm. Simulations run on a modern CPU clocked at 3.2 GHz show the throughput increase from 14 Kbps to 6.3 Mbps for a polar code of length 1024. This idea is then extended to allow for a tunable number of decoder memories instantiated, mitigating the increase in computational complexity while providing modest increase in throughput. Third, an early termination criterion is investigated that is shown to reduce the number of bit estimates by up to 58%. Finally, the benefits of the fast simplified successive cancellation list decoder are extended to the stack algorithm, resulting in the first reported implementation of a fast simplified successive cancellation stack decoder that reports a throughput of up to 20.44 Mbps." --
Author: Harsh Aurora
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
"Error correcting codes are essential in realizing reliable communication over noisy channels. Polar codes are a recent class of linear block error correcting codes, and are the first of their kind to have an explicit construction and asymptotically achieve the symmetric channel capacity over binary-input discrete memoryless channels. They have recently been adopted into the 5G standard in the eMBB control channel. The successive cancellation list decoding algorithm yields near-optimal decoding performance at the cost of high implementation complexity. The successive cancellation stack algorithm has been shown to provide similar decoding performance at a much lower computational complexity, but suffers from a large memory requirement that scales quadratically with the code length, rendering it impractical in most applications. This thesis presents several approaches to increase the practicality of the successive cancellation stack decoding algorithm in software implementations. First, multiple copies of decoder memory are replaced with a single memory, and the stack sorting step is replaced by a linear search. While this comes at the cost of an increase in computational complexity, results show that the large memory requirement and sorting are amongst primary culprits in the mediocre throughput performance of the software stack algorithm. Simulations run on a modern CPU clocked at 3.2 GHz show the throughput increase from 14 Kbps to 6.3 Mbps for a polar code of length 1024. This idea is then extended to allow for a tunable number of decoder memories instantiated, mitigating the increase in computational complexity while providing modest increase in throughput. Third, an early termination criterion is investigated that is shown to reduce the number of bit estimates by up to 58%. Finally, the benefits of the fast simplified successive cancellation list decoder are extended to the stack algorithm, resulting in the first reported implementation of a fast simplified successive cancellation stack decoder that reports a throughput of up to 20.44 Mbps." --
Author: Pascal Giard
Publisher: Springer
ISBN: 3319597825
Category : Computers
Languages : en
Pages : 108
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Book Description
A new class of provably capacity achieving error-correction codes, polar codes are suitable for many problems, such as lossless and lossy source coding, problems with side information, multiple access channel, etc. The first comprehensive book on the implementation of decoders for polar codes, the authors take a tutorial approach to explain the practical decoder implementation challenges and trade-offs in either software or hardware. They also demonstrate new trade-offs in latency, throughput, and complexity in software implementations for high-performance computing and GPGPUs, and hardware implementations using custom processing elements, full-custom application-specific integrated circuits (ASICs), and field-programmable-gate arrays (FPGAs). Presenting a good overview of this research area and future directions, High-Speed Decoders for Polar Codes is perfect for any researcher or SDR practitioner looking into implementing efficient decoders for polar codes, as well as students and professors in a modern error correction class. As polar codes have been accepted to protect the control channel in the next-generation mobile communication standard (5G) developed by the 3GPP, the audience includes engineers who will have to implement decoders for such codes and hardware engineers designing the backbone of communication networks.
Author: Adam Cavatassi
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
"In 2008, a new class of block error correction codes, known as polar codes, were provenby Erdal Arıkan to be able to achieve the Shannon limit. Through inventive new de-coding algorithms and fast code constructions, polar codes have become an attractivehigh-performance error correction code for practical use. These innovations have resultedin adoption of polar codes in the upcoming 3GPP 5 th generation standard for New Ra-dio. Still, polar codes are hindered by certain inflexible characteristics. Arıkan's originalpolar code definition limits block lengths to powers of two, due to a recursive Kroneckerproduct of the 2 × 2 polarizing kernel. This constraint presents a considerable obstacle,as many realistic scenarios call for all code lengths to be readily available. Rate-matchingtechniques, known as puncturing and shortening, allow for flexible polar code lengths,albeit with inefficient decoding complexity. Multi-kernel polar codes produce native codelengths that are powers of two and/or three with the addition of a 3 × 3 ternary kernel,although they necessitate specialized decoders and code design. This thesis will exploreand propose techniques that are intended for maximizing the flexibility and efficiencyof polar codes, as well as analyze any trade-offs affecting error correction performance.An in-depth study is presented that compares state-of-the-art length-flexible polar codeswith the 3GPP standardized polar codes. This inquiry finds that the 5G standard offersa highly simplified polar code construction with minimal loss to error correction per-formance. Further, multi-kernel polar codes were found to have a negative correlationbetween error correction performance and the quantity of ternary Kronecker constituents.This thesis also proposes a new fast successive cancellation decoder that is compliant withmulti-kernel polar codes. The ternary kernel is further investigated by testing its rate-matching and systematic properties. Finally, this thesis proposes a new scheme calledasymmetric polar codes. We present details on generator matrix definition, informa-tion set design, and decoding schedules, as well as perform comparisons with competingschemes using simulations and a comprehensive analysis. Asymmetric polar codes offerflexible block lengths with decoding complexity lower than equivalent length-compatiblepolar codes under successive cancellation. The enclosed findings indicate that asymmetricpolar codes afford comparable error correction performance to the competing schemes,while dividing the number of successive cancellation decoding operations by up to a fac-tor of two. The thesis is then concluded by recommending appropriate extensions of thiswork for future research." --
Author: Gabi Sarkis
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
"Error-correcting codes enable reliable and efficient data communication and storage and have become an indispensable part of information processing systems. Polar codes are the latest discovery in the quest for more powerful error correction. They are the first codes with an explicit construction to provably achieve the symmetric capacity of memoryless channels. Moreover, this performance is realizable using the low complexity successive-cancellation decoding algorithm. Despite their attractive theoretical properties, polar codes suffer from two major issues hindering practical implementations: a slow decoding algorithm and mediocre error-correction performance at moderate code lengths. Solutions to these problems in the literature have been mutually exclusive. Decoding speed can be increased, but at the cost of degrading error-correction capability. On the other hand, the error-correction performance can be greatly improved using a list decoding algorithm, which incurs a large cost in both decoding speed and memory requirements. This incompatibility in solutions must be resolved before polar codes become practical. This thesis presents novel, compatible solutions to these problems. It introduces a new decoding algorithm that has the same error-correction performance as successive cancellation, but offers significantly lower latency and higher throughput. A corresponding decoder implementation is shown to be an order of magnitude faster than the state-of-the-art in the literature. Next, the speed of successive-cancellation list decoders for polar codes is improved without degrading error-correction performance. The resulting software decoders implementing the proposed algorithm offer throughput and error-correction performance exceeding the best in the literature and meeting the requirements for the 802.11n WiFi standard. This work also brings to light another beneficial property of polar codes that had not been studied before. It presents encoders and decoders that can operate on polar codes of any length and rate, while maintaining low implementation complexity and fast operating speed. Such implementations are important in systems that must adapt to varying channel conditions. Finally, two methods are introduced that improve error-correction performance without incurring the memory overhead of list decoding. The first targets systems where re-transmission is impossible or highly undesirable. The second improves the performance of software decoders using polar codes with rates very close to the channel capacity." --
Author: Furkan Ercan
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
"Polar codes are a class of error-correcting codes that can provably achieve the channel capacity and have simple encoding and decoding mechanisms. Due to their attractive properties, the interest in polar codes has been increasing rapidly in recent years and they have been adopted for use in the $5^{\text{th}}$ generation (5G) wireless systems standard. Specifically, they have been chosen as the coding scheme for the control channel of enhanced mobile broadband (eMBB) use case, and they are being considered for other use cases within 5G. Successive cancellation (SC) decoding is the primary decoding algorithm of polar codes and has low implementation complexity. The two main problems of SC decoding is its mediocre error-correction performance at practical codeword lengths and its long latency due to its sequential nature. To overcome the latency problem, fast decoding techniques have been introduced to speed up the decoding process by an order of magnitude. Secondly, several SC-based decoding algorithms have been proposed to improve the decoding performance, such as SC-List (SCL) and SC-Flip (SCF) decoding. SCL decoding uses parallel SC decoders to improve error-correction performance and therefore suffers from high implementation complexity. On the other hand, the SCF decoding algorithm uses multiple iterations of SC decoding to improve error-correction performance and maintains a similar implementation complexity to that of SC decoding. Therefore, SCF is a promising low-complexity alternative to SCL decoding.This thesis covers several improvements for SC and SCF-based polar decoders. First, we describe how to utilize the hardware resources of fast SC decoding more efficiently and show how to improve the throughput. Second, we propose a partitioned decoding scheme for the SCF algorithm that is able to improve the error-correction performance and reduce the average number of iterations. Third, we describe how to implement energy-efficient polar decoders using fast SC and fast SCF algorithms. We propose the first fast SCF decoder in hardware and show that an energy-efficient approach with improved throughput is possible. Then, we describe the Thresholded SCF (TSCF) algorithm, which has improved error-correction performance and less computational complexity than the conventional SCF algorithm. We implement fast decoding techniques to create the Fast-TSCF decoder that is able to outperform decoders of similar performance in terms of throughput and area efficiency. Finally, we describe many simplifications and optimizations for the Dynamic SCF (DSCF) decoding algorithm, which is known for its significantly improved error-correction performance but has impractical computations. We replace its transcendental computations with simple approximations, introduce fast decoding techniques, reduce its computational complexity by using a theoretical framework, and demonstrate with hardware implementation. The proposed practical DSCF implementation is able to match the error-correction performance and throughput of SCL-based decoders with large list sizes and stands as a low-complexity alternative"--
Author: Seyyed Ali Hashemi
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
"Polar codes have received a great deal of attention in the past few years to the extent that they are selected to be included in the 5th Generation of Wireless Communications Standard (5G). Specifically, polar codes were selected as the coding scheme for the Enhanced Mobile Broadband (eMBB) control channel which requires codes of short length. The main bottleneck in the deployment of polar codes in 5G is the design of a decoder which can achieve good error-correction performance, with low hardware implementation cost and high throughput. Successive-Cancellation (SC) decoding was the first algorithm under which polar codes could achieve capacity when the code length is very high. However, for finite practical code lengths, SC decoding falls short in providing a reasonable error-correction performance because of its sub-optimality with respect to the Maximum-Likelihood (ML) decoder. Sphere Decoding (SD) is an algorithm that can achieve the performance of ML decoding with a very high complexity. In order to close the gap between SC and ML decoding, Successive-Cancellation List (SCL) decoding keeps a list of candidates and selects the one with the best Path Metric (PM). Although SCL provides a good error-correction performance, it comes at the cost of higher complexity and lower throughput. In this thesis, we first propose a low complexity SD algorithm which provides a good trade-off between the error-correction performance and the complexity of the decoder for polar codes of short lengths. We then propose algorithms to speed up the SCL decoders. We prove that while these algorithms have much higher throughput than the conventional SCL decoder, they incur no error-correction performance loss. We further propose several techniques to reduce the area occupation in the hardware implementation of SC and SCL decoders by reducing their memory requirements. We solve the flexibility issue of fast SC-based decoders and introduce a completely rate-flexible scheme. Hardware architectures for the proposed algorithms are presented and comparisons with state of the art are made. Finally, we evaluate the performance of polar codes in 5G and we show that polar codes can be used in practical applications by proposing a blind detection scheme with polar codes." --
Author: Orhan Gazi
Publisher:
ISBN: 9789811307386
Category : Coding theory
Languages : en
Pages :
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Book Description
This book explains the philosophy of the polar encoding and decoding technique. Polar codes are one of the most recently discovered capacity-achieving channel codes. What sets them apart from other channel codes is the fact that polar codes are designed mathematically and their performance is mathematically proven. The book develops related fundamental concepts from information theory, such as entropy, mutual information, and channel capacity. It then explains the successive cancellation decoding logic and provides the necessary formulas, moving on to demonstrate the successive cancellation decoding operation with a tree structure. It also demonstrates the calculation of split channel capacities when polar codes are employed for binary erasure channels, and explains the mathematical formulation of successive cancellation decoding for polar codes. In closing, the book presents and proves the channel polarization theorem, before mathematically analyzing the performance of polar codes.
Author: Brian W. Kernighan
Publisher: Addison-Wesley Professional
ISBN: 0133133419
Category : Computers
Languages : en
Pages : 283
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Book Description
With the same insight and authority that made their book The Unix Programming Environment a classic, Brian Kernighan and Rob Pike have written The Practice of Programming to help make individual programmers more effective and productive. The practice of programming is more than just writing code. Programmers must also assess tradeoffs, choose among design alternatives, debug and test, improve performance, and maintain software written by themselves and others. At the same time, they must be concerned with issues like compatibility, robustness, and reliability, while meeting specifications. The Practice of Programming covers all these topics, and more. This book is full of practical advice and real-world examples in C, C++, Java, and a variety of special-purpose languages. It includes chapters on: debugging: finding bugs quickly and methodically testing: guaranteeing that software works correctly and reliably performance: making programs faster and more compact portability: ensuring that programs run everywhere without change design: balancing goals and constraints to decide which algorithms and data structures are best interfaces: using abstraction and information hiding to control the interactions between components style: writing code that works well and is a pleasure to read notation: choosing languages and tools that let the machine do more of the work Kernighan and Pike have distilled years of experience writing programs, teaching, and working with other programmers to create this book. Anyone who writes software will profit from the principles and guidance in The Practice of Programming.
Author: Keisuke Fujii
Publisher: Springer
ISBN: 981287996X
Category : Science
Languages : en
Pages : 148
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Book Description
This book presents a self-consistent review of quantum computation with topological quantum codes. The book covers everything required to understand topological fault-tolerant quantum computation, ranging from the definition of the surface code to topological quantum error correction and topological fault-tolerant operations. The underlying basic concepts and powerful tools, such as universal quantum computation, quantum algorithms, stabilizer formalism, and measurement-based quantum computation, are also introduced in a self-consistent way. The interdisciplinary fields between quantum information and other fields of physics such as condensed matter physics and statistical physics are also explored in terms of the topological quantum codes. This book thus provides the first comprehensive description of the whole picture of topological quantum codes and quantum computation with them.
Author: Marco Dorigo
Publisher: MIT Press
ISBN: 9780262042192
Category : Computers
Languages : en
Pages : 324
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Book Description
An overview of the rapidly growing field of ant colony optimization that describes theoretical findings, the major algorithms, and current applications. The complex social behaviors of ants have been much studied by science, and computer scientists are now finding that these behavior patterns can provide models for solving difficult combinatorial optimization problems. The attempt to develop algorithms inspired by one aspect of ant behavior, the ability to find what computer scientists would call shortest paths, has become the field of ant colony optimization (ACO), the most successful and widely recognized algorithmic technique based on ant behavior. This book presents an overview of this rapidly growing field, from its theoretical inception to practical applications, including descriptions of many available ACO algorithms and their uses. The book first describes the translation of observed ant behavior into working optimization algorithms. The ant colony metaheuristic is then introduced and viewed in the general context of combinatorial optimization. This is followed by a detailed description and guide to all major ACO algorithms and a report on current theoretical findings. The book surveys ACO applications now in use, including routing, assignment, scheduling, subset, machine learning, and bioinformatics problems. AntNet, an ACO algorithm designed for the network routing problem, is described in detail. The authors conclude by summarizing the progress in the field and outlining future research directions. Each chapter ends with bibliographic material, bullet points setting out important ideas covered in the chapter, and exercises. Ant Colony Optimization will be of interest to academic and industry researchers, graduate students, and practitioners who wish to learn how to implement ACO algorithms.
