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.

Polar codes are the first family of error-correcting codes that was proved to achieve the capacity of binary memoryless symmetric (BMS) channels with efficient encoding and decoding algorithms. They have been drawing increasing interests in both industrial and academic research, especially after being adopted by the 3rd generation partnership project (3GPP) group as the channel codes for the control channel of the 5th generation (5G) wireless systems. The main goal of this dissertation is to explore polar coding techniques, as well as improve the current state-of-the-art, thereby broadening the applications of polar codes. We begin by studying partial orders (POs) for the synthesized bit-channels of polar codes. We give an alternative proof of an existing PO for bit-channels with the same Hamming weight and use the underlying idea to extend the bit-channel ordering to some additional cases. The bit-channels with universal ordering positions for binary erasure channel (BEC), which are independent of the channel erasure probability, are verified for all of the code blocklengths. We also show the threshold behavior of the Bhattacharyya parameters of some bit-channels by approximating the threshold values. Then, we move on to the decoding algorithms and improved polar codes. Despite the impressive asymptotic behavior by channel polarization, empirical results indicate less impressive performance of the successive cancellation (SC) decoder for polar codes of short blocklengths, e.g., compared to low-density parity-check (LDPC) codes. We consider belief propagation list (BPL) decoding with a special family of factor-graph layer permutations called stable permutations (SPs) that preserve a specified information set when the corresponding bit permutations are applied to message bit indices. Then, we propose a new code construction methodology to interpolate between Reed-Muller (RM) and polar codes. The new family of hybrid RM-polar codes has superior performance under several decoding algorithms, including SC list (SCL), belief propagation (BP), BPL, and soft-cancellation list (SCANL). By taking advantage of an existing PO on bit-channels whose corresponding indices share the same Hamming weight, we analyze the complexity of the new construction method. Furthermore, we propose an algorithm of BP decoding for polar codes with a special family of large kernels called permuted kernels, in which the leftmost messages over the factor graph need to be permuted accordingly.

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.

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.

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 discusses the latest channel coding techniques, MIMO systems, and 5G channel coding evolution. It provides a comprehensive overview of channel coding, covering modern techniques such as turbo codes, low-density parity-check (LDPC) codes, space–time coding, polar codes, LT codes, and Raptor codes as well as the traditional codes such as cyclic codes, BCH, RS codes, and convolutional codes. It also explores MIMO communications, which is an effective method for high-speed or high-reliability wireless communications. It also examines the evolution of 5G channel coding techniques. Each of the 13 chapters features numerous illustrative examples for easy understanding of the coding techniques, and MATLAB-based programs are integrated in the text to enhance readers’ grasp of the underlying theories. Further, PC-based MATLAB m-files for illustrative examples are included for students and researchers involved in advanced and current concepts of coding theory.

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.