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."

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.

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.

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.

A comprehensive review to the theory, application and research of machine learning for future wireless communications In one single volume, Machine Learning for Future Wireless Communications provides a comprehensive and highly accessible treatment to the theory, applications and current research developments to the technology aspects related to machine learning for wireless communications and networks. The technology development of machine learning for wireless communications has grown explosively and is one of the biggest trends in related academic, research and industry communities. Deep neural networks-based machine learning technology is a promising tool to attack the big challenge in wireless communications and networks imposed by the increasing demands in terms of capacity, coverage, latency, efficiency flexibility, compatibility, quality of experience and silicon convergence. The author – a noted expert on the topic – covers a wide range of topics including system architecture and optimization, physical-layer and cross-layer processing, air interface and protocol design, beamforming and antenna configuration, network coding and slicing, cell acquisition and handover, scheduling and rate adaption, radio access control, smart proactive caching and adaptive resource allocations. Uniquely organized into three categories: Spectrum Intelligence, Transmission Intelligence and Network Intelligence, this important resource: Offers a comprehensive review of the theory, applications and current developments of machine learning for wireless communications and networks Covers a range of topics from architecture and optimization to adaptive resource allocations Reviews state-of-the-art machine learning based solutions for network coverage Includes an overview of the applications of machine learning algorithms in future wireless networks Explores flexible backhaul and front-haul, cross-layer optimization and coding, full-duplex radio, digital front-end (DFE) and radio-frequency (RF) processing Written for professional engineers, researchers, scientists, manufacturers, network operators, software developers and graduate students, Machine Learning for Future Wireless Communications presents in 21 chapters a comprehensive review of the topic authored by an expert in the field.

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.

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.