Polarization and Polar Codes

Polarization and Polar Codes

Polarization and Polar Codes

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."

New Frontiers in Polar Coding

New Frontiers in Polar Coding

New Frontiers in Polar Coding

The discovery of channel polarization and polar codes is universally recognized as an historic breakthrough in coding theory. Polar codes provably achieve the capacity of any memoryless symmetric channel, with low encoding and decoding complexity. Moreover, for short block lengths, polar codes under specific decoding algorithms are currently the best known coding scheme for binary-input Gaussian channels. Due to this and other considerations, 3GPP has recently decided to incorporate polar codes in the 5G wireless communications standard. Soon enough, a remarkably short time after their invention, we will be all using polar codes whenever we make a phone call or access the Internet on a mobile device. Our goal in this dissertation is to explore new frontiers in polar coding, thereby fundamentally advancing the current state-of-the-art in the field. Parts of the results are immediately relevant for successful deployment of polar codes in wireless systems, whereas other parts will focus on key theoretical problems in polar coding that have a longer time-horizon. We begin by studying the effect of the polarization kernels in the asymptotic behavior of polar codes. We show that replacing the conventional 2×2 kernel in the construction of polar codes with that of a larger size can reduce the gap to the capacity if the larger kernel is carefully selected. A heuristic algorithm is proposed that helps to find such kernels. Furthermore, we prove that a near-optimal scaling behavior is achievable if one is allowed to increase the kernel size as needed. We also study the computational complexity of decoding algorithms for polar codes with large kernels, which are viewed as their main implementation obstacle. Moving on to the decoding algorithms, we carefully analyze the performance of the successive cancellation decoder with access to the abstract concept of Arikan's genie. The CRC-aided successive-cancellation list decoding, the primary decoding method of polar codes, is commonly viewed as an implementation of the Arikan's genie. However, it comes short at completely simulating the genie since the auxiliary information (CRC) comes to the help only at the end of the decoding process. We overcome this problem by introducing the convolutional decoding algorithm of polar codes that is based on a high-rate convolutional pre-coder and utilizes Viterbi Algorithm to mimic the genie all the way through the SC decoding process. Lastly, we look into channels with deletions. A key assumption in the traditional polar coding is to transmit coded symbols over independent instances of the communication channel. Channels with memory and in particular, deletion channels, do not follow this rule. We introduce a modified polar coding scheme for these channels that depend on much less computational power for decoding than the existing solutions. We also extend the polarization theorems to provide theoretical guarantee and to prove the correctness of our algorithms.

Channel Coding Techniques for 5G Using Polar Codes

Channel Coding Techniques for 5G Using Polar Codes

Channel Coding Techniques for 5G Using Polar Codes

Coding and modulation in the crown known as the communications technology, embodies a national basic theory of the overall strength of communication science. Channel coding is a way of encoding data in a communication channel that adds patterns of redundancy into the transmission path in order to lower the error rate. Such methods are widely used in wireless communications. 5G is the coming fifth-generation wireless broadband technology based on the IEEE 802.11ac standard. 5G will provide better speeds and coverage than the current 4G. It operates with a 5 Ghz signal and is set to offer speeds of up to 1 Gb/s for tens of connections or tens of Mb/s for tens of thousands of connections. Commonly accepted use cases for 5G networks are eMBB (Enhanced Mobile Broadband), Massive IoT (Internet of Things) and URLLC (UltraReliable and Low Latency Communications). eMBB covers Internet access with high data rates to enable rich media applications, cloud storage and applications, and augmented reality for entertainment. All these demanding scenarios make use of many 5G standards of which polar codes is used as the channel coding scheme for eMBB scenario as short codes for control channel. A new class of codes, polar codes, recently made a breakthrough in coding theory. In 2008, Erdal Arıkan at Bilkent University invented polar codes, providing a new mathematical framework to solve this problem. The construction itself was first described by Stolte, and later independently by Erdal Arıkan in 2008 This thesis focuses on study of the key technology of polar code including the construction encoding and decoding. In this work, we analyze a method, known as channel polarization, to construct block codes that achieve the symmetric capacity of any binary-input discrete memoryless channel (B-DMC). The proof of their capacity achieving property is also given. In particular, we show that the algorithm can find almost all the “good” channels with computing complexity which is essentially linear in block-length. This thesis explores the structure and features of polar codes to improve their performance using Gaussian approximation-based construction of polar codes. Several schemes of polar codes are compared with each other like successive cancellation decoding(SC), list decoding(LS), list decoding with CRC(LS+CRC) and finally the existing adaptive decoder is shown to outperform all the schemes.

Polar Codes

Polar Codes

Polar Codes

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.

Kernels of Polar Codes and Their Applications to Wireless Channels and Joint Source and Channel Coding Based on LDPC Codes

Kernels of Polar Codes and Their Applications to Wireless Channels  and Joint Source and Channel Coding Based on LDPC Codes

Kernels of Polar Codes and Their Applications to Wireless Channels and Joint Source and Channel Coding Based on LDPC Codes

This dissertation contains three topics: Polar codes with optimal exponents based on linear and nonlinear binary kernels of sizes up to 16, a design of rate-compatible polar codes, and a new proposed structure of joint source and channel coding based on low-density-parity-check (LDPC) codes. Polar codes are proposed by Arıkan with construction based on a linear kernel of dimension 2 with polarizing properties. The performance of a polar code is characterized asymptotically in terms of the exponent of its kernel. In this dissertation, constructions of linear and nonlinear binary kernels of dimensions up to 16 are presented. The constructed kernels are proved to have maximum exponents except in the case of nonlinear kernels of dimension 12 where we show that there exists only one possible exponent greater than that of the presented construction. From the results, the minimum dimension where a linear kernel with exponent greater than 0.5, the exponent of the linear kernel proposed by Arıkan, is 15, while this minimum dimension is 14 for nonlinear kernels. We also found that there is a linear kernel with maximum exponent up to dimension 11. The kernels of dimensions 13, 14, 15 with maximum exponents, although nonlinear over GF(2), are shown to be Z4-linear or Z2Z4-linear. In addition to exploring the asymptotic behavior of polar codes, we propose a design of finite block length rate-compatible polar codes suitable for HARQ communications. The central feature of the proposed design is established on the puncturing order chosen with low complexity on a base code of short length, which is then extended to the desired length. With the designed puncturing order, a practical rate-matching system which can be adjusted to any desired rate through puncturing or repetition under polarization is suggested. The proposed rate-matching system combines a channel interleaver and a bit-mapping procedure to preserve the polarization of the rate-compatible polar code family under bit-interleaved coded modulation systems. Simulation results on AWGN and fast fading channels with different modulation orders in both Chase combining and incremental redundancy HARQ communications are listed. For the third topic, we investigate a joint source and channel LDPC coding scheme in which the source compression and the channel coding matrices are designed jointly as two submatrices of a sparse matrix H. The sparse matrix H is constructed algebraically with a structure free of cycles of length 4 and serves as the parity-check matrix for joint decoding of the channel output symbols and untransmitted source symbols. The integrated design of the source and channel coding matrices strengthens the information exchange between the source symbols and the channel output parity-check symbols, which provides a good waterfall error performance of the coded system and low error-foor.

Towards Practical Length compatible Polar Codes

Towards Practical Length compatible Polar Codes

Towards Practical Length compatible Polar Codes

"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." --

Communications and Networking

Communications and Networking

Communications and Networking

This two volume set constitutes the refereed proceedings of the 14th EAI International Conference on Communications and Networking, ChinaCom 2019, held in November/December 2019 in Shanghai, China. The 81 papers presented were carefully selected from 162 submissions. The papers are organized in topical sections on Internet of Things (IoT), antenna, microwave and cellular communication, wireless communications and networking, network and information security, communication QoS, reliability and modeling, pattern recognition and image signal processing, and information processing.

Wireless Internet

Wireless Internet

Wireless Internet

This book constitutes the refereed post-conference proceedings of the 10th International Conference on Wireless Internet , WiCON 2017, held in Tianjin, China, in December 2017. The 42 full papers were selected from 70 submissions and cover the following topics: wireless networking, massive MIMO and mmWave, WSNs and VANETs, security and IoT, wireless communications, cloud and big data networking.

Smart Cities Performability Cognition Security

Smart Cities Performability  Cognition    Security

Smart Cities Performability Cognition Security

This book provides knowledge into the intelligence and security areas of smart-city paradigms. It focuses on connected computing devices, mechanical and digital machines, objects, and/or people that are provided with unique identifiers. The authors discuss the ability to transmit data over a wireless network without requiring human-to-human or human-to-computer interaction via secure/intelligent methods. The authors also provide a strong foundation for researchers to advance further in the assessment domain of these topics in the IoT era. The aim of this book is hence to focus on both the design and implementation aspects of the intelligence and security approaches in smart city applications that are enabled and supported by the IoT paradigms. Presents research related to cognitive computing and secured telecommunication paradigms; Discusses development of intelligent outdoor monitoring systems via wireless sensing technologies; With contributions from researchers, scientists, engineers and practitioners in telecommunication and smart cities.

High Speed Decoders for Polar Codes

High Speed Decoders for Polar Codes

High Speed Decoders for Polar Codes

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.