The weight spectrum plays a crucial role in the performance of error-correcting codes. Pre-transformation with an upper-triangular matrix improves the weight spectrum of polar codes while retaining polarization. However, a theoretical analysis to quantify the improvement for pre-transformed rate-compatible polar codes is missing. In this paper, we calculate the average spectrum of random upper-triangular pre-transformed shortened and punctured polar codes. Our approach tran-scends the limitations imposed by partial ordering and specific rate matching patterns. A key feature of our approach is its polynomial complexity in relation to the code length, making it computationally feasible. Simulation results affirm that our findings provide an accurate approximation on the performance of pre-transformed rate-compatible polar codes.

In this paper, we establish the partial orders (POs) of rate-compatible polar codes under both the binary erasure channel (BEC) and the binary memoryless symmetric channel (BMSC). Firstly, we define the POs for rate-compatible polar codes under block rate matching. Additionally, we demonstrate that certain POs for mother code lengths remain valid under rate matching in the BEC. Finally, leveraging the existing POs in the BEC, we derive POs in the BMSC under block rate matching.

The weight spectrum plays a crucial role in the performance of error-correcting codes. Despite substantial theoretical exploration into polar codes with mother code length, a framework for the weight spectrum of rate-compatible polar codes remains elusive. In this paper, we address this gap by enumerating the number of minimum-weight codewords for quasi-uniform punctured, Wang-Liu shortened, and bit-reversal shortened decreasing polar codes. Notably, our algorithms operate with polynomial complexity relative to the code length. Simulation results affirm that our discoveries provide an accurate approximation on the performance of rate-compatible polar codes.

In this paper, we study the lossless analog compression fori.i.d.discrete-continuous mixed signals via the polarization-based framework. We prove that for discrete-continuous mixed source, the error probability of maximum a posteriori (MAP) estimation polarizes under the Hadamard transform, which extends the polarization phenomenon to analog domain. Building on this insight, we propose the partial Hadamard compression and develop the corresponding analog successive cancellation (SC) decoder. The proposed scheme consists of deterministic measurement matrices and non-iterative reconstruction algorithm, providing benefits in both space and computational complexity. Using the polarization of error probability, we prove that our approach achieves the information-theoretical limit for lossless analog compression developed by Wu and Verdú.

This paper investigates the random access capacity in low-earth-orbit mega-constellation. We establish a novel methodology by considering key components, e.g., preamble collision and detection procedures. Leveraging on the system-level simulation platform, we study the impact of latitudes, user density, and random access channel resources on the random access capability. Simulation results reveal that the number of successfully connected users saturates with the growth of user density, and the sat-uration point is around 260 users per second. Furthermore, satellite-centric and user-centric coverage approaches are discussed, and the latter is preferable in terms of the signal-to-interference-plus-noise ratio. In addition, we propose the non-uniform broadcast beam sweeping scheme, and the total access capacity gain of 33.31% is achieved compared to the uniform baseline.

Low Earth orbit (LEO) mega-constellation satellite networks have shown great potential to extend the coverage capability of conventional terrestrial networks. How to systematically define, quantify, and assess the technical performance of LEO mega-constellation satellite networks remains an open issue. In this paper, we propose a comprehensive key performance indica-tor (KPI) framework for mega-constellation based LEO satellite networks. An efficient LEO constellation oriented performance evaluation methodology is then carefully designed by resorting to the concept of interfering area and spherical geographic cell. We have carried out rigorous system-level simulations and provided numerical results to assess the KPI framework. It can be observed that the achieved area traffic capacity of the reference LEO constellation is around 4 Kbps/km2, with service availability ranging from 0.36 to 0.39. Besides, the average access success probability and handover failure rate is approximate to 96% and 10%, respectively, in the nearest satellite association scheme.

In this paper, we establish the second-order randomized identification capacity (RID capacity) of the Additive White Gaussian Noise Channel (AWGNC). On the one hand, we obtain a refined version of Hayashi's theorem to prove the achievability part. On the other, we investigate the relationship between identification and channel resolvability, then we propose a finer quantization method to prove the converse part. Consequently, the second-order RID capacity of the AWGNC has the same form as the second-order transmission capacity. The only difference is that the maximum number of messages in RID scales double exponentially in the block length.

In this paper, we define partial orders (POs) of polar codes based on the Bhattacharyya parameter and the bit-error probability, respectively. These POs are applicable to arbitrary binary memoryless symmetric channel (BMSC). Leveraging the extremal inequalities of polarization transformation, we derive new POs for BMSC based on the corresponding POs observed in the Binary Erasure Channel (BEC). We provide examples that demonstrate the inability of existing POs to deduce these novel POs. Furthermore, we establish upper bounds for the expansion parameter$\beta$if the polar codes constructed by$\beta- \mathbf{expansion}$method obey these POs.

Elementary trapping sets (ETSs) are the principal culprits for the performance of LDPC codes in the error floor region. Due to their large quantity, intricate structures, and high computational complexity, determining how to eliminate dominant ETSs in the design of LDPC codes has become a critical issue in improving error floor behavior. In this paper, we address this problem by avoiding particular theta graphs$(\theta(1,2,2)$and$\theta(2,2,2))$in the Tanner graph to eliminate specific ETSs. These can be characterized by a pivotal tool in graph theory - Turán numbers. Theoretically, we derive the exact Turán number for$\theta(1,2,2)$and demonstrate that all$(a, b)$-ETSs in a Tanner graph with variable-reaular degree$d_{L}(v)=\gamma$must satisfy the inequality$b\geq a\gamma-\frac{1}{2}a^{2}$. This result improves the lower bound previously obtained by Amirzade when the girth is 6. For girth 8, by constraining the relationship between any two 8-cycles in the Tanner graph, we establish a similar inequality$b\geq a\gamma-\frac{a(\sqrt{8a-7}-1)}{2}$. Our simulation results indicate that codes designed with these considerations exhibit improved performance and a lower error floor over additive white Gaussian noise channels.

Unequal error protection (UEP) codes can facilitate the transmission of messages with different protection levels. In this paper, we study the achievability bounds on UEP by the generalization of Gilbert-Varshamov (GV) bound. For the first time, we show that under certain conditions, UEP enhances the code rate comparing with time-sharing (TS) strategies asymptotically.

The number of low-weight codewords is critical to the performance of error-correcting codes. In 1970, Kasami and Tokura characterized the codewords of Reed-Muller (RM) codes whose weights are less than 2wmin, wherewminrepresents the minimum weight. In this paper, we extend their results to decreasing polar codes. We present the closed-form expressions for the number of codewords in decreasing polar codes with weights less than 2wmin. Moreover, the proposed enumeration algorithm runs in polynomial time with respect to the code length.

The automorphism ensemble (AE) decoding framework for polar codes attracts much attention recently. It decodes multiple permuted codewords with successive cancellation (SC) decoders in parallel and hence has lower latency compared to successive cancellation list (SCL) decoding. However, the AE decoding framework is ineffective for permutations falling into the lower-triangular affine (LTA) automorphism group, as they are invariant under SC decoding. Therefore, the block lower-triangular affine (BLTA) group was discovered to achieve better AE decoding performance. However, the equivalence of the BLTA group and the complete affine automorphism group was unresolved. Additionally, some automorphisms in BLTA group are also SC-invariant, thus are redundant in AE decoding. In this paper, we prove that BLTA group coincides with the complete automorphisms of decreasing polar codes that can be formulated as affine transformations. Also, we find a necessary and sufficient condition related to the block lower-triangular structure of transformation matrices to identify SC-invariant automorphisms. Furthermore, We present an algorithm that efficiently identifies all SC-invariant affine automorphisms under specific constructions.

In this paper, we study the lossless analog compression for i.i.d. nonsingular signals. Through analyzing analog polarization under Hadamard transform, we propose efficient successive cancellation (SC) decoding algorithm over analog domain. Thanks to the polarization of Rényi information dimension (RID) and the absorption of discrete entropy, we prove that the proposed scheme achieves the information-theoretical limit for lossless analog compression developed by Wu and Verdú.

Pre-transformation with an upper-triangular matrix (including cyclic redundancy check (CRC), parity-check (PC) and polarization-adjusted convolutional (PAC) codes) improves the weight spectrum of Reed-Muller (RM) codes and polar codes significantly. However, a theoretical analysis to quantify the improvement is missing. In this paper, we provide asymptotic analysis on the number of low-weight codewords of the original and pre-transformed RM codes respectively, and prove that pre-transformation significantly reduces low-weight codewords, even in the order sense. For polar codes, we prove that the average number of minimum-weight codewords does not increase after pre-transformation. Both results confirm the advantages of pre-transformation.

Targeting high-throughput and low-power communications, we implement two successive cancellation (SC) decoders for polar codes. Converted to 16nm ASIC technology, the area efficiency and energy efficiency are 4Tbps/mm2and 0.63pJ/bit, respectively, for the unrolled decoder, and 561Gbps/mm2and 1.21pJ/bit, respectively, for the recursive decoder. To achieve such a high throughput, a novel code construction, coined as fast polar codes, is proposed and jointly optimized with a highly-parallel SC decoding architecture. First, we reuse existing modules to fast decode more outer code blocks, and then modify code construction to facilitate faster decoding for all outer code blocks up to a degree of parallelism of 16. Furthermore, parallel comparison circuits and bit quantization schemes are customized for hardware implementation. Collectively, they contribute to an 2.66× area efficiency improvement and 33% energy saving over the state of the art.

The rapid development of Internet of Things (IoT) requires new massive random access protocols to support the massive devices. Recently, Polyanskiy [1] established an information-theoretic formulation of unsourced multiple access (uMAC) problem and proposed theoretical finite-length achievability and converse bounds. In this paper, we further study the tradeoff between the number of active users and the energy-per-bit of random Gaussian codebook under maximum likelihood decoding and use two methods to improve the finite-length achievability bounds when the number of users is large and small, respectively. Our new results improve the finite-length achievability bound by more than 0.15 dB when per-user probability of error (PUPE) is 10−1, and more than 0.25 dB when PUPE is 10−3.

Satellite communication by leveraging the use of low earth orbit (LEO) satellites is expected to play an essential role in future communication systems through providing ubiquitous and continuous wireless connectivity. This thus has motivated the work in the 3rd generation partnership project (3GPP) to ensure the operation of fifth generation (5G) New Radio (NR) protocols for non-terrestrial network (NTN). In this paper, we consider a NR-based LEO satellite communication system, where satellites equipped with phased array antennas are employed to serve user equipments (UEs) on the ground. To reduce payload weight and meet the time-varying traffic demands of UEs, an efficient beam hopping scheme considering both the traffic demands and inter-beam interference is proposed to jointly schedule beams and satellite transmit power. Then based on NR protocols, we present the first system-level evaluations of beam hopping scheme in LEO satellite system under different operating frequency bands and traffic models. Simulation results indicate that significant performance gains can be achieved by the proposed beam hopping scheme, especially under the distance limit constraint that avoids scheduling adjacent beams simultaneously, as compared to benchmark schemes.

In this paper, we design a polar decoding platform for diverse application scenarios that require low-cost and low-power communications. Specifically, prevalent polar decoders such as successive cancellation (SC), SC-list (SCL) and Fano decoders are all supported under the same architecture. Unlike high-throughput or low-latency decoders that promote parallelism, this architecture promotes serialization by repeatedly calling a “sub-process” that is executed by a core module. Surprisingly, the resulting serial SCL-8 decoder is only 3 times the size of an SC decoder, much smaller than the predicted 8 times. Cost and power are minimized through resource sharing and adaptive decoding techniques, etc. We carried out performance simulation and hardware implementation to evaluate the actual chip area and energy consumption.

Automorphism ensemble (AE) decoding for polar codes was proposed by decoding permuted codewords with successive cancellation (SC) decoders in parallel and hence has lower latency compared to that of successive cancellation list (SCL) decoding. However, some automorphisms are SC-invariant, thus are redundant in AE decoding. In this paper, we find a necessary and sufficient condition related to the block lower-triangular structure of transformation matrices to identify SC-invariant automorphisms. Furthermore, we provide an algorithm to determine the complete SC-invariant affine automorphisms under a specific polar code construction.

Identification capacities of randomized and deterministic identification were proved to exceed channel capacity for Gaussian channels with channel side information (CSI). In this work, we extend deterministic identification to the block fading channels without CSI by applying identification codes for both channel estimation and user identification. We prove that identification capacity is asymptotically higher than transmission capacity even in the absence of CSI. And we also analyze the finite-length performance theoretically and numerically. The simulation results verify the feasibility of the proposed blind deterministic identification in finite blocklength regime.

Recently, a permutation-based successive cancellation (PSC) decoding framework for polar codes attracts much attention. It decodes several permuted codewords with indepen-dent successive cancellation (SC) decoders. Its latency thus can be reduced to that of SC decoding. However, the PSC framework is ineffective for permutations falling into the lower-triangular affine (LTA) automorphism group, as they are invariant under SC decoding. As such, a larger block lower-triangular affine (BLTA) group that contains SC-variant permutations was discovered for decreasing polar codes. But it was unknown whether BLTA equals the complete automorphism group. In this paper, we prove that BLTA equals the complete automorphisms of decreasing polar codes that can be formulated as affine transformations.

Polar codes are the first class of channel codes achieving the symmetric capacity of the binary-input discrete memoryless channels (B-DMC) with efficient encoding and decoding algorithms. But the weight spectrum of polar codes is relatively poor compared to Reed-Muller (RM) codes, which degrades their maximum-likehood (ML) performance. Pre-transformation with an upper-triangular matrix (including cyclic redundancy check (CRC), parity-check (PC) and polarization-adjusted convolutional (PAC) codes), improves weight spectrum while retaining polarization. In this paper, the weight spectrum of upper-triangular pre-transformed polar codes is mathematically analyzed. In particular, we focus on calculating the number of low-weight codewords due to their impact on error-correction performance. Simulation results verify the accuracy of the analysis.

To improve the system performance towards the Shannon limit, advanced radio resource management mechanisms play a fundamental role. In particular, scheduling should receive much attention, because it allocates radio resources among different users in terms of their channel conditions and QoS requirements. The difficulties of scheduling algorithms are the tradeoffs need to be made among multiple objectives, such as throughput, fairness and packet drop rate. We propose a smart scheduling scheme based on deep reinforcement learning (DRL). We not only verify the performance gain achieved, but also provide implementation-friend designs, i.e., a scalable neural network design for the agent and an offline training framework. With the scalable neural network design, the DRL agent can easily handle the cases when the number of active users is time-varying without the need to redesign and retrain the DRL agent. Training the DRL agent offline first and using it as the initial version in the practical usage help to prevent the system from suffering from performance and robustness degradation due to the time-consuming training. Through both simulations and field tests, we show that the DRL-based smart scheduling outperforms the conventional scheduling method and can be adopted in practical systems.

This paper investigates the impact of beamforming codebook update period on the signal to noise ratio (SNR) performance of low earth orbit (LEO) earth-fixed beams. To combat the SNR degradation due to non-timely beam updates, we propose the combined algorithm of beam angle compensation and dynamic codebook prediction. The proposed algorithm is able to constraint the SNR degradation at the target under a designed threshold.

Recently, a parallel decoding algorithm of GN-coset codes was proposed. The algorithm exploits two equivalent decoding graphs. For each graph, the inner code part, which consists of independent component codes, is decoded in parallel. The extrinsic information of the code bits is obtained and iteratively exchanged between the graphs until convergence. This algorithm enjoys a higher decoding parallelism than the previous successive cancellation algorithms, due to the avoidance of serial outer code processing. In this work, we present a hardware implementation of the parallel decoding algorithm, it can support maximum N = 16384. We complete the decoder's physical layout in TSMC 16nm process and the size is 999.936μm×999.936μm, ≈ 1.00mm2. The decoder's area efficiency and power consumption are evaluated for the cases of N = 16384, K = 13225 and N = 16384, K = 14161. Scaled to 7nm process, the decoder's throughput is higher than 477Gbps/mm2and 533Gbps/mm2with five iterations.

Recently, a parallel decoding framework of GN-coset codes was proposed. High throughput is achieved by decoding the independent component polar codes in parallel. Various algorithms can be employed to decode these component codes, enabling a flexible throughput-performance tradeoff. In this work, we adopt successive cancellation (SC) as the component decoders to achieve the highest-throughput end of the tradeoff. The benefits over soft-output component decoders are reduced complexity and simpler (binary) interconnections among component decoders. To reduce performance degradation, we integrate an error detector and a log-likelihood ratio (LLR) generator into each component decoder. The LLR generator, specifically the damping factors therein, is designed by a genetic algorithm. This low-complexity design can achieve an area efficiency of 533Gbps/mm2under 7nm technology.

Polar codes has been selected as the channel coding scheme for 5G new radio (NR) control channel. Specifically, a special type of parity-check polar (PC-Polar) codes was adopted in uplink control information (UCI). In this paper, we propose a parity-check soft-cancellation (PC-SCAN) algorithm and its simplified version to decode PC-Polar codes. The potential benefits are two-fold. First, PC-SCAN can provide soft output for PCPolar codes, which is essential for advanced turbo receivers. Second, the decoding performance is better than that of successive cancellation (SC). This is due to the fact that paritycheck constraints can be exploited by PC-SCAN to enhance the reliability of other information bits over the iterations. Moreover, we describe a cyclic-shift-register (CSR) based implementation "CSR-SCAN" to reduce both hardware cost and latency with minimum performance loss.

In this work, we propose a type of GN-coset codes for parallel decoding. The parallel decoder exploits two equivalent decoding graphs of GN-coset codes. For each decoding graph, the inner code part is composed of independent component codes to be decoded in parallel. The extrinsic information of the code bits is obtained and iteratively exchanged between the two graphs until convergence. Accordingly, we explore a heuristic and flexible code construction method (information set selection) for various information lengths and coding rates. Compared to the previous successive cancellation algorithm, the parallel decoder avoids the serial outer code processing and enjoys a higher degree of parallelism. Furthermore, a flexible trade-off between performance and decoding latency can be achieved with three types of component decoders. Simulation results demonstrate that the proposed encoder-decoder framework achieves comparable error correction performance to polar codes with a much lower decoding latency.

In this paper, the downlink packet scheduling problem for cellular networks is modeled, which jointly optimizes throughput, fairness and packet drop rate. Two genie-aided heuristic search methods are employed to explore the solution space. A deep reinforcement learning (DRL) framework with Advantage actor-critic (A2C) algorithm is proposed for the optimization problem. Several methods have been utilized in the framework to improve the sampling and training efficiency and to adapt the algorithm to a specific scheduling problem. Numerical results show that DRL outperforms the baseline algorithm and achieves similar performance as genie-aided methods without using the future information.

The applications of artificial intelligence (AI) and machine learning (ML) technologies in wireless communications have drawn significant attention recently. AI has demonstrated real success in speech understanding, image identification, and natural language processing domains, thus exhibiting its great potential in solving problems that cannot be easily modeled. AI techniques have become an enabler in wireless communications to fulfill the increasing and diverse requirements across a large range of application scenarios. In this paper, we elaborate on several typical wireless scenarios, such as channel modeling, channel decoding and signal detection, and channel coding design, in which AI plays an important role in wireless communications. Then, AI and information theory are discussed from the viewpoint of the information bottleneck. Finally, we discuss some ideas about how AI techniques can be deeply integrated with wireless communication systems.

In this paper, we investigate an artificial-intelligence (AI) driven approach to design error correction codes (ECC). Classic error-correction code design based upon coding-theoretic principles typically strives to optimize some performance-related code property such as minimum Hamming distance, decoding threshold, or subchannel reliability ordering. In contrast, AI-driven approaches, such as reinforcement learning (RL) and genetic algorithms, rely primarily on optimization methods to learn the parameters of an optimal code within a certain code family. We employ a constructor-evaluator framework, in which the code constructor can be realized by various AI algorithms and the code evaluator provides code performance metric measurements. The code constructor keeps improving the code construction to maximize code performance that is evaluated by the code evaluator. As examples, we focus on RL and genetic algorithms to construct linear block codes and polar codes. The results show that comparable code performance can be achieved with respect to the existing codes. It is noteworthy that our method can provide superior performances to classic constructions in certain cases (e.g., list decoding for polar codes).

In this paper, we model nested polar code construction as a Markov decision process (MDP), and tackle it with advanced reinforcement learning (RL) techniques. First, an MDP environment with state, action, and reward is defined in the context of polar coding. Specifically, a state represents the construction of an (N, K) polar code, an action specifies its reduction to an (N, K - 1) subcode, and the reward is the decoding performance. A neural network architecture consisting of both policy and value networks is proposed to generate actions based on the observed states, aiming at maximizing the overall rewards. A loss function is defined to trade off between exploitation and exploration. To further improve learning efficiency and quality, an “integrated learning” paradigm is proposed. It first employs a genetic algorithm to generate a population of (sub-)optimal polar codes for each (N, K), and then uses them as prior knowledge to refine the policy of RL. Such a paradigm is shown to accelerate the training process, and converge at better performances. Simulation results show that the proposed learning-based polar constructions achieve comparable, or even better, performances than the state of the art under successive cancellation list (SCL) decoders, and meanwhile satisfies the nested property. Last but not least, the learning process does not exploit explicit expert knowledge from polar coding theory.

Accurate prediction of fading channel in the upcoming transmission frame is essential to realize adaptive transmission for transmitters, and receivers with the ability of channel prediction can also save some computations of channel estimation. However, due to the rapid channel variation and channel estimation error, reliable prediction is hard to realize. In this situation, an appropriate channel model should be selected, which can cover both the statistical model and small scale fading of channel, this reminds us the natural languages, which also have statistical word frequency and specific sentences. Accordingly, in this paper, we take wireless channel model as a language model, and the time-varying channel as talking in this language, while the realistic noisy estimated channel can be compared with mumbling. Furthermore, in order to utilize as much as possible the information a channel coefficient takes, we discard the conventional two features of absolute value and phase, replacing with hundreds of features which will be learned by our channel model, to do this, we use a vocabulary to map a complex channel coefficient into an ID, which is represented by a vector of real numbers. Recurrent neural networks technique is used as its good balance between memorization and generalization, moreover, we creatively introduce sequence-to-sequence (seq2seq) models in time series channel prediction, which can translate past channel into future channel. The results show that realistic channel prediction with superior performance relative to channel estimation is attainable.

The key to successive cancellation (SC) flip decoding of polar codes is to accurately identify the first error bit. The optimal flipping strategy is considered difficult due to lack of an analytical solution. Alternatively, we propose a deep learning aided SC flip algorithm. Specifically, before each SC decoding attempt, a long short-term memory (LSTM) network is exploited to either (i) locate the first error bit, or (ii) undo a previous "wrong" flip. In each SC attempt, the sequence of log likelihood ratios (LLRs) derived in the previous SC attempt is exploited to decide which action to take. Accordingly, a two-stage training method of the LSTM network is proposed, i.e., learn to locate first error bits in the first stage, and then to undo "wrong" flips in the second stage. Simulation results show that the proposed approach identifies error bits more accurately and achieves better block error rate performance than the state-of-the-art SC flip algorithms.

A special permutation group of polar codes based on$N$/4-cyclic shift is designed and analyzed for practical use. A permutation-transformation equivalence is firstly introduced to transfer the effect of permutation on the codeword side to the uncoded side. Then, we introduce the$N$/4-cyclic shift permutation and analyze the conditions under which it can permute a codeword to another for polar codes that even do not fully respect partial order. We also reveal that the value assignment of frozen bits should follow specific rules related to the permutation pattern. Finally, a novel polar-specific implicit indication method is presented by applying the$N$/4-cyclic shift permutation group to the practical wireless communication scenarios such as Physical Broadcasting Channel (PBCH) of a cellular network, which significantly simplifies the detection algorithm.

In this paper, we propose a comprehensive Polar coding solution that integrates reliability calculation, rate matching and parity-check coding. Judging a channel coding design from the industry's viewpoint, there are two primary concerns: (i) low-complexity implementation in application-specific integrated circuit (ASIC), and (ii) superior \& stable performance under a wide range of code lengths and rates. The former provides cost- \& power-efficiency which are vital to any commercial system; the latter ensures flexible and robust services. Our design respects both criteria. It demonstrates better performance than existing schemes in literature, but requires only a fraction of implementation cost. With easily-reproducible code construction for arbitrary code rates and lengths, we are able to report ``1-bit'' fine-granularity simulation results for thousands of cases. The released results can serve as a baseline for future optimization of Polar codes.

Polarization weight (PW) is a novel construction method for polar codes, which results in universal reliability ordering efficiently and yields imilar performance as other channel dependent construction methods. In this paper, we interpret PW method or algorithm from a rate allocation perspective of channel polarization to show its effectiveness. Take the AWGN channel as an example, we show that the rate allocation for information bits by PW method coincides with the capacities of channel polarization. Furthermore, some properties of PW algorithm, including the universal and fractal of the reliability ordering, are illustrated, which facilitate the implementation in practice. Comprehensive simulation results with various code rates, code lengths and list sizes are also shown to validate the effectiveness of PW method.

Polar codes are the first proven capacity-achieving codes. Recently, they are adopted as the channel coding scheme for 5G due to their superior performance. A polar code for encoding length-K information bits in length-N codeword could be specified by the polar code construction method. Most construction methods define a polar code related to channel parameter set, e.g. designed signal-to-noise ratio. Polarization weight (PW) is a channel-independent approximation method, which estimates the subchannel reliability as a function of its index. In this paper, we generalize the PW method by including higher-order bases or extended bases. The proposed methods have robust performance while preserving the computational and mathematical simplicity as PW.

In this work, we introduce β-expansion, a notion borrowed from number theory, as a theoretical framework to study fast construction of polar codes based on a recursive structure of universal partial order (UPO) and polarization weight (PW) algorithm. We show that polar codes can be recursively constructed from UPO by continuously solving several polynomial equations at each recursive step. From these polynomial equations, we can extract an interval for β, such that ranking the synthetic channels through a closed- form β-expansion preserves the property of nested frozen sets, which is a desired feature for low- complex construction. In an example of AWGN channels, we show that this interval for β converges to a constant close to 1.1892 when the code block-length trends to infinity. Both asymptotic analysis and simulation results validate our theoretical claims.

We propose to use second order Reed-Muller (RM) sequence for user identification in 5G grant-free access. The benefits of RM sequences mainly lie in two folds, (i) support of much larger user space, hence lower collision probability and (ii) lower detection complexity. These two features are essential to meet the massive connectivity (107links/km2), ultra-reliable and low-latency requirements in 5G, e.g., one-shot transmission (≤ Ims) with ≤ 10-4packet error rate. However, the nonorthogonality introduced during sequence space expansion leads to worse detection performance. In this paper, we propose a noiseresilient detection algorithm along with a layered sequence construction to meet the harsh requirements. Link-level simulations in both narrow-band and OFDM-based scenarios show that RM sequences are suitable for 5G.

Spectral efficiency is always a key factor to be improved and optimized along mobile communication networks evolving generation by generation. 5G enabling technologies must take spectral efficiency into consideration. In this paper, we show the performance of three key 5G technologies in sense of spectral efficiency improvement. Sparse code multiple access, polar codes, and filtered orthogonal frequency-division multiplexing are novel multiple access technology, channel coding scheme, and waveform, respectively. The combination of them is implemented in a 5G field trial testbed by NTT DOCOMO and Huawei for the first time. According to the field test results, we achieve over 100% spectral efficiency improvement comparison with baseline, where orthogonal frequency-division multiple access and turbo coding as LTE are used.

5G IoT communications have some new requirements on the whole system design, e.g., low cost, low power consumption, long distance coverage and massive connection. To fulfill all these requirements, a narrow-band SCMA scheme is proposed. Narrow band pulse shaping is employed, so that the coverage can be expanded with low-cost and low-power devices. Two types of waveforms are provided, both of which use SCMA to enlarge the number of supported devices. Simulation results show that, comparing to the existing narrow band techniques, narrow-band SCMA scheme can support more dense connectivity without any other performance degradation.