Polar Codes

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Polar Codes

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Author : Orhan Gazi
language : en
Publisher: Springer
Release Date : 2018-06-08

Polar Codes written by Orhan Gazi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-08 with Technology & Engineering categories.

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.

High Speed Decoders For Polar Codes

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Author : Pascal Giard
language : en
Publisher: Springer
Release Date : 2017-08-30

High Speed Decoders For Polar Codes written by Pascal Giard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-30 with Computers categories.

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.

Polar Codes From Theory To Practice

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Author : Rowshan
language : en
Publisher: Wiley-Blackwell
Release Date : 2024-09-26

Polar Codes From Theory To Practice written by Rowshan and has been published by Wiley-Blackwell this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-26 with categories.

Polar Codes For Data Storage And Communication Network Applications

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Author : Karthik Nagarjuna Tunuguntla
language : en
Publisher:
Release Date : 2022

Polar Codes For Data Storage And Communication Network Applications written by Karthik Nagarjuna Tunuguntla and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.

The dissertation provides polar coding techniques for a variety of source and channel models with applications to storage and communication networks. We first provide universal polar codes for asymmetric compound channels that avoid common randomness. A staircase alignment of polar blocks is considered in the code construction. An MDS code is used in each column achieving the universality and a scrambling technique is implemented for each column helping avoid common randomness. These compound asymmetric channels are used for modelling flash-memories, such as MLCs (multi-level cell flash memories), and TLCs (three-level cell flash memories) memories. Hence the proposed universal polar codes for asymmetric channels can be used for flash memory error correction. The costly noiseless channel model was used to model a flash memory device. Each of the voltage levels to which a flash memory cell can be programmed has an associated wear cost which reflects the damage caused to the cell by repeated programming to that level. Shaping codes that minimize the average cost per channel symbol for a specified rate and shaping codes that minimize the average cost per source symbol (i.e., the total cost) have been shown to reduce cell wear and increase the lifetime of the memory. Hence, we study polar shaping codes for costly noiseless channels minimizing total cost. We also study polar shaping codes for costly noisy channels for the design of efficient codes that combine wear reduction and error correction for use in a noisy flash memory device. A novel scheme based on polar codes is proposed to compress a uniform source when a side information correlated with the source is available at the receiver while the conditional distribution of the side information given the source is symmetric and unknown to the source. An adaptation of universal polar codes with an incorporation of the linear code duality between channel coding and Slepian-Wolf coding is used in the design of those codes. Optimal rate is achieved through the proposed codes for the source model. These codes can be used in a wireless sensor network where the measurements tracked at two different nodes are correlated and the correlation may not always be fixed due to environmental changes such as weather. The nodes communicate the information sensed or measured by them to a central location. Finally, we provide a capacity-achieving polar coding strategy on a multi-level 3-receiver broadcast channel in which the second receiver is degraded (stochastically) from the first receiver for the transmission of a public message intended for all the receivers and a private message intended for the first receiver. A chaining strategy, translating the ideas of superposition coding, rate-splitting and indirect coding into polar coding, is used in the construction. The codes designed for such a channel model and setting can be used for video and audio file transfer in a client-server network where the individual clients are a computer and two mobile phones. The two mobile phone clients just support audio application where the computer supports both audio and video applications.

Towards Practical Length Compatible Polar Codes

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Author : Adam Cavatassi
language : en
Publisher:
Release Date : 2019

Towards Practical Length Compatible Polar Codes written by Adam Cavatassi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.

"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." --

Polarization And Polar Codes

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Author : Eren Şaşoǧlu
language : en
Publisher: Now Pub
Release Date : 2012

Polarization And Polar Codes written by Eren Şaşoǧlu and has been published by Now Pub this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Computers categories.

Polarization and Polar Codes: A Tutorial is the first in-depth tutorial on this exciting new technique that promises to offer major improvements in digital communications systems."

Topics In Polar Coding

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Author : Hanwen Yao
language : en
Publisher:
Release Date : 2022

Topics In Polar Coding written by Hanwen Yao and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.

The discovery of polar codes has been widely acknowledged as one of the most original and profound breakthroughs in coding theory in the recent two decades. Polar codes form the first explicit family of codes that provably achieves Shannon's capacities with efficient encoding and decoding for a wide range of channels. This solves one of the most fundamental problems in coding theory. At the beginning of its invention, polar code is more recognized as an intriguing theoretical topic due its mediocre performance at moderate block lengths. Later, with the invention of the list decoding algorithm and various other techniques, polar codes now show competitive, and in some cases, better performance as compared with turbo and LDPC codes. Due to this and other considerations, the 3rd Generation Partnership Project (3GPP) has selected polar codes for control and physical broadcast channels in the enhanced mobile broadband (eMBB) mode and the ultra-reliable low latency communications (URLLC) mode of the fifth generation (5G) wireless communications standard. In this dissertation, we propose new theories on a wide range of topics in polar coding, including structural properties, construction methods, and decoding algorithms. We begin by looking into the weight distribution of polar codes. As an important characteristic for an error correction code, weight distribution directly gives us estimations on the maximum-likelihood decoding performance of the code. In this dissertation, we present a deterministic algorithm for computing the entire weight distribution of polar codes. We first derive an efficient procedure to compute the weight distribution of polar cosets, and then show that any polar code can be represented as a disjoint union of such polar cosets. We further study the algebraic properties of polar codes as decreasing monomial codes to bound the complexity of our approach. Moreover, we show that this complexity can be drastically reduced using the automorphism group of decreasing monomial codes. Next, we dive into the topic of large kernel polar codes. It has been shown that polar codes achieve capacity at a rather slow speed, where this speed can be measured by a parameter called scaling exponent. One way to improve the scaling exponent of polar codes, is by replacing their conventional 2x2 kernel with a larger polarization kernel. In this dissertation, we propose theories and a construction approach for a special type of large polarization kernels to construct polar codes with better scaling exponents. Our construction method gives us the first explicit family of codes with scaling exponent provably under 3. However, large kernel polar codes are known for their high decoding complexity. In that respect, we also propose a new decoding algorithm that can efficiently perform successive cancellation decoding for large kernel polar codes. Moving on to the decoding algorithms, we focus ourselves on a new family of codes called PAC codes, recently introduced by Arikan, that combines polar codes with convolutional precoding. At short block lengths such as 128, PAC codes show better performance under sequential decoding compared with conventional polar codes with CRC precoding. In this dissertation, we first show that we can achieve the same superior performance of PAC codes using list decoding with relatively large list sizes. Then we carry out a qualitative complexity comparison between sequential decoding and list decoding for PAC codes. Lastly, we look into the subject of polar coded modulation. Bit-interleaved coded modulation (BICM) and multilevel coded modulation (MLC) are two ways commonly used to combine polar codes with high order modulation. In this dissertation, we propose a new hybrid polar coded modulation scheme that lies between BICM and MLC. For high order modulation, our hybrid scheme has a latency advantage compared with MLC. And by simulation we show that our hybrid scheme also achieves a considerable performance gain compared with BICM.