This paper presents a comprehensive review/tutorial on multi-functional metasurfaces integrated with M-type ferrite materials for millimeter-wave (mmWave) absorption and beam control. As wireless communication systems transition toward beyond-5G architectures, including non-terrestrial networks (NTNs), the demand for adaptive, low-profile electromagnetic surfaces that can manage interference while enabling beam reconfiguration becomes increasingly critical. Conventional metasurfaces often struggle to simultaneously achieve high absorption and beamforming over wide frequency ranges due to intrinsic material and structural limitations. This paper reviews the state-of-the-art in metasurface design for dual-functionality— particularly those combining frequency-selective magnetic materials with periodic surface lattices—to enable passive, compact, and reconfigurable reflectors and absorbers. Special emphasis is placed on the role of M-type ferrites in enhancing absorption via ferromagnetic resonance (FMR), and on the use of surface-wave trapping mechanisms to achieve narrowband and broadband functionality. A case study of a ferrite-based hybrid “reflectsorber” (reflectrarray + absorber) is presented to demonstrate key design concepts, analytical models, and application scenarios relevant to satellite, UAV, and NTN ground station deployments. Future directions for low-loss, tunable, and scalable metasurfaces in next-generation wireless infrastructures are also discussed.

We propose a polar coding scheme for block fading channels, aiming to achieve maximum diversity while maintaining the performance under additive white Gaussian noise channels (AWGNC). The key idea isdiversity alignment, which aligns maximum diversity with information bits through proper codeword bit to fading block mapping. We first develop a low-complexity diversity analysis tool based on Boolean approximation under genie-aided successive cancellation decoding which can be used for arbitrary bit-to-block mapping. Second, we propose a tractable optimal block mapping forM= 2 fading blocks and develop fast search algorithms for generalM≥ 2, achieving optimal low-rate diversity coding (dc=MatR= 1/M) for a wide range ofM. Moreover, our scheme can be applied to achieve optimal high-rate diversity-2 coding (dc= 2 atR= (M−1)/M) with good AWGNC codes. We show that appropriate block-mapping can achieve both low-rate and high-rate optimal diversity simultaneously. Numerical results demonstrate that our framework provides accurate diversity analysis and the proposed DA scheme outperforms conventional interleavers under block fading channels while preserving AWGNC performance. The proposed can play a crucial role in supporting the URLLC communication in future systems, where channel is quickly changing but high reliability is required.

With the advent of extreme massive multiple-input multiple-output (X-MIMO) systems and the emerging Frequency Range 3 (FR3, 7.125–24.25 GHz) for 6G networks, the dimensionality of channel state information (CSI) has increased significantly. However, to ensure scalable operation and avoid an excessive increase in overhead, the feedback size is expected to increase only marginally. This constraint necessitates an extremely high compression ratio during CSI feedback, which in turn severely degrades the reconstruction performance of standardized codebooks. Moreover, even when employing AI methods, training models from scratch under such severe compression conditions leads to vanishing or exploding gradients, resulting in unstable training and diminished performance. In this paper, we propose a novel hierarchical transfer learning with progressive compression (HTL-PC) method to address these challenges. Our approach leverages a pretrained autoencoder extraction block from a large-feedback model and progressively transfers it to models with smaller latent spaces, thereby enabling stable training under severe compression conditions. Extensive system-level simulations demonstrate that the proposed HTL-PC method achieves remarkable improvements in squared generalized cosine similarity and downlink cell throughput over benchmark techniques.

To mitigate the growing overhead resulting from the increasing number of antennas in massive multiple-input multiple-output (MIMO) systems, various autoencoder-based schemes employing two-sided artificial intelligence (AI) models for channel state information (CSI) feedback-specifically, feedback of the precoding matrix-have been proposed. In these twosided AI models, the encoder and decoder are separately deployed at the user equipment (UE) and the base station (BS), posing significant challenges in maintaining synchronization between them in real-world scenarios with multiple UEs and BSs. In this paper, we propose a novel transformer-based temporaldomain multi-length optimized (TMO) decoder that effectively leverages temporal correlations in MIMO channels to enhance CSI reconstruction. Unlike existing schemes that require different models or additional signaling overhead for re-synchronization between the encoder and decoder under varying conditions, the transformer-based TMO decoder can robustly recover CSI by utilizing feedback of the precoding matrix with temporal information using a single fixed model for inputs of varying sequential time steps. Performance evaluations demonstrate that the proposed transformer-based TMO decoder achieves significantly higher squared generalized cosine similarity and average downlink throughput compared to state-of-the-art techniques.

Block Orthogonal Sparse Superposition (BOSS) codes are a promising class of joint coded modulation techniques that can closely approach the finite-blocklength capacity with low-complexity decoding at low code rates under Gaussian channels. However, in fading channels, the performance of BOSS codes degrades considerably due to varying channel fading effects on coded symbols. This paper presents a unified approach to extending BOSS codes to practical fading scenarios and introduces novel joint demodulation and decoding solutions. For fast-fading channels, we propose a minimum mean square error approximation maximum a posteriori (MMSE-A-MAP) algorithm that integrates demodulation and decoding when channel state information is available at the receiver (CSIR). Additionally, for block-fading channels without CSIR, we introduce a joint demodulation and decoding method, referred to as the non-coherent sphere decoding (NSD) algorithm. Simulation results demonstrate that BOSS codes with MMSE-A-MAP decoding outperform 5G polar codes, while the NSD algorithm achieves performance comparable to quasi-maximum likelihood decoding but with significantly reduced complexity. Both decoding methods can be implemented for parallel processing, allowing them to meet low-latency requirements. Furthermore, real-time simulations on a software-defined radio testbed validate the feasibility of using BOSS codes for low-power transmission.

In the realm of mobile communications, the receiver often encounters undesired situations where it receives only noise, interference, or unintended signals. In such cases, it may incorrectly infer that the decoding result is valid, particularly when the error detection capability, mainly provided by a cyclic redundancy check (CR C) code, falls short. While bounded distance decoding techniques based on the employed error-correcting code have been introduced to address this issue, there is still room for improvement especially when dealing with unintended signals. In this paper, we present a formula to identify the situation of unintended signals and find it expressed in terms of a metric called discrepancy. Utilizing this discrepancy, we interpret the problem of determining the validity of decoding results as a binary classification task. Then, we propose suitable machine learning techniques to improve the accuracy of the binary classification process. Our experimental results, conducted for the 5G New Radio (NR) system, demonstrate significant performance improvement resulting from the application of the proposed methods.

We address the suboptimality of successive cancellation (SC) decoding for polar codes, which is caused by treating as random variables all the future bits to be estimated later. For a target information bit, we define the frozen and parity bits located behind it as its future constraints (FCs). To incorporate FCs into the sequential decoding of the target bit, we propose two elementary techniques: an SC check (SCC) algorithm and an FC conversion rule enabling belief propagation (BP). Focusing on the binary erasure channel (BEC), we also present a tree search technique based on stack-based backjumping (SBJ) to efficiently solve dynamic constraint satisfaction problems (CSP) formulated by FCs. Numerical results show that the combination of BP and SCC decoding algorithms accompanied with the SBJ technique achieves excellent erasure recovery performance over the BEC, which is close to the dependence testing (DT) achievability bound.

This paper presents an analytically designed layered decoding algorithm for quasi-cyclic low-density parity-check (QC-LDPC) codes in the 5th Generation (5G) New Radio (NR) mobile communication system. First, a layered density evolution (DE) based on reciprocal channel approximation (RCA) is newly developed to accurately reflect the layered decoding operation in the decoder design. Using this technique, a single nested sequence is optimized in a greedy way to configure the processing order for any given number of layers. The error-correction performance is improved by up to 0.15 dB, while the number of iterations is reduced by about one simultaneously.

This paper presents density evolution (DE) techniques based on reciprocal channel approximation (RCA) for general bit-interleaved coded modulation (BICM) systems. The original RCA-based DE (RCA-DE) technique is implemented under the assumption of binary-input additive white Gaussian noise channels (BI-AWGNCs). In BICM systems, however,$M$-ary modulation schemes are generally used, and they can be regarded as to be a parallel transmission of$\log _{2} M$bits. Thus,$\log _{2} M$separate bit-level channels, which are not Gaussian equivalent, need to be considered. In order to extend the conventional RCA-DE technique to BICM systems, we first establish a model of protograph BICM ensembles. Two methods are developed based on the bit error rate (BER) and the BICM capacity in order to find a corresponding BI-AWGNC that models each of the bit-level channels. Using these methods, we implement the protograph RCA-DE technique for BICM systems and show that it achieves an accurate estimation. As a practical application of the proposed RCA-DE method, we design bit interleavers in order to achieve better BICM performance in the 3GPP New Radio (NR) LDPC coding system. Numerical results show that performance gain of up to 0.3 dB is consistently achieved over a wide range of parameter values.

Concatenated polar codes under successive cancellation list (SCL) decoding have excellent error-correction performance. However, their expected error-detection capability becomes degraded, when we increase the list size of the SCL decoder in order to improve their error-correction performance. In this paper, we propose a configuration design scheme for the SCL decoder and a post-decoding validation check scheme in order to provide a better tradeoff between error-detection and error-correction performance. Firstly, a configuration of the SCL decoder is designed to improve its own error detection capability. Specifically, a part of dynamic frozen bits (also called parity-check bits) is used for path checking during SCL decoding rather than their original purpose of use, path pruning. Furthermore, the number of paths to be checked by the applied cyclic redundancy check (CRC) code is limited. Secondly, a new metric corresponding to the correlation between the received signal vector and the decoded one is presented to check the validity of the decoding result. These proposed schemes are analyzed to provide a proper configuration of the SCL decoder and determine a threshold for post-decoding validation check. Numerical results show that a better tradeoff between error correction and detection is achieved, compared with conventional schemes.

Shaped polar codes were recently proposed to improve the spectral efficiency of polar coded modulation, based on probabilistic shaping. The key principle for them is to adjust the probability of occurrence of 1's in each codeword by introducing the shaping bits, which makes the distribution of modulated symbols close to the Gaussian distribution. But, they have a serious problem from a practical viewpoint, since additional polar decoding is required to determine the shaping bits. In this paper, we investigate an algebraic approach to the design of structurally shaped polar codes. We first select a shaping set in an algebraic and systematic way and determine the shaping bits by using simple binary and integer operations without any additional polar decoding. We then propose a method to construct structurally shaped polar codes, and analyze their shaped probability in an approximate way. Finally, we present the encoding and decoding procedures for the proposed shaped polar codes. Numerical results show that the proposed shaping scheme has similar performance than the conventional shaping scheme regardless of whether cyclic redundancy check is employed, while the former can be implemented in an extremely simpler way than the latter.

In blind detection, the user equipment attempts to decode a set of candidate groups to find its own control information. False alarm (FA) refers to an event in which decoding is successful even though a signal is not transmitted, and is one of several critical issues occurring in a blind detection problem. For CRC-aided polar code, with the limited number of CRC bits, FA occurs when the CRC check passes even though there is no signal. In this paper, we propose a technique to efficiently reduce FA events using two detection metrics which are specially suited to low rate and high rate codes. Simulation results show that the application of the proposed DMs outperform the conventional schemes. To be specific, at high rates, the proposed scheme reduces 90% of FA compared to the standard CRC-based detection.

In this paper, we introduce a structural extension method of polar codes as a new code modification method. Structural extension is a systematic method of generating additional codeword bits from the mother code by selecting intermediate bits obtained in the middle of the polar encoding. We start by studying simplex-extension from a 2×2 local polarization kernel, and then, we generalize this method to construct polar codes of arbitrary lengths. This extension method does not change the original polar code structure, and thus, the conventional encoder and decoder can be employed with a slight modification. We present a code construction tool by modifying density evolution to design punctured, shortened, and extended polar codes. By analysis and numerical experiments, we show that the proposed structural extension method enables to achieve an excellent tradeoff between performance and implementation complexity.

In this paper, we investigate the fundamentals of puncturing and shortening for polar codes, based on binary domination which plays a key role in polar code construction. We first prove that the orders of encoder input bits to be made incapable (by puncturing) or to be shortened are governed by binary domination. In particular, we show that binary domination completely determines incapable or shortened bit patterns for polar codes, and that all the possible incapable or shortened bit patterns can be identified. We then present the patterns of the corresponding encoder output bits to be punctured or fixed, when the incapable or shortened bits are given.

In this paper, we investigate the fundamentals of puncturing and shortening for polar codes, based on binary domination. For punctured and shortened polar codes, we prove that the partial order by binary domination completely determines both incapable bit patterns (by puncturing) and fixed bit patterns (by shortening). In particular, we give a necessary and sufficient condition for an encoder output bit to be fixed by additionally shortening a single encoder input bit, as well as a necessary and sufficient condition for an encoder input bit to be made incapable by additionally puncturing a single encoder output bit. We also identify all the puncturing bit patterns yielding a given incapable bit pattern. These results provide a guidance to design a practical rate-matching scheme for polar codes. As an example, we present a rate-matching scheme based on our analytical observations. Numerical results show that it performs well over a wide range of code lengths and rates, compared with conventional rate-matching schemes.

An integer-forcing (IF) linear multiple-input multiple-output (MIMO) receiver has recently been proposed, which is theoretically shown to achieve near capacity with almost the same complexity as that of conventional linear receivers. The key idea is that the receiver attempts to directly decode integer-linear combinations of codewords. To ensure that this sum-decoding operation is feasible, in previous works, lattice codes over$\mathbb {Z}_{q}$were employed. Although those codes can attain good theoretical performance, however, its implementation complexity can be considerably high in practice, especially when$q$is large to support high-order modulations. In this paper, we propose a practical multilevel coding scheme for IF MIMO, in which multilevel encoding composed of binary linear codes$(q = 2)$in conjunction with the natural mapping is employed on the transmitter side and multistage decoding adapted to the IF operation is employed on the receiver side. The performance of the proposed scheme is extensively evaluated both analytically and numerically, showing that the gain of IF over conventional receivers is indeed achievable in practical settings with almost the same complexity. Our results imply that the proposed IF MIMO can be an attractive solution for the 5G communications due to its ability of supporting high spectral efficiency with low complexity.

The effect of imperfect channel state information (CSI) on rate adaptation in time-varying multi-antenna fading channels is studied. In the presence of feedback delay and channel estimation error, we analyze the outage probability (OP), defined as the average probability that the achievable rate in the current channel state is lower than data rate scheduled based on outdated feedback, for maximum ratio combining receivers in single-input multiple-output channels and zero-forcing (ZF) receivers in multiple-input multiple-output (MIMO) channels. In particular, for temporally correlated MIMO channels, the conditional distribution of SNR at the output of ZF detection in the current channel state is unknown; hence we apply a Gaussian approximation to obtain a closed-form expression for the average OP of the MIMO-ZF receiver. Simulation results show that our derivations are well-matched to the actual OP and throughput of multi-antenna rate adaptive systems. Also, based on our analysis results, we propose a simple rate adaptation scheme that maximizes the average throughput under a target OP constraint. The proposed schemes optimize the scheduled rate according to a given CSI condition, and effectively maximize the average outage-constrained throughput.

This paper deals with the randomness of depth-2 connectivity of LDPC ensembles. We study how the randomness of LDPC graphs affect asymptotic performance over binary erasure channel (BEC). First, a new attribute, degree-spectrum distribution, is defined to specify the connectivity of more detailed ensembles than those defined by degree distribution. With this, specified ensembles become subsets of conventional ensemble, and we develop a new density evolution method. Some extreme cases of specified ensembles are given, and we prove that the random specified ensemble is better than other regularized types.

In this paper, we introduce new attributes of low-density parity-check graphs, degree-set and degree-sum, which explains the connectivity of a check node with more detail. Then, we consider more specified ensembles defined by degree-set/sum distribution of the graph than one defined by the degree distribution. As the degree set/sum distribution varies, tradeoff between the performance at the waterfall and that at the error-floor is observed. The trade-off point can be managed by controlling degree-set/sum distribution.

In this paper, we analyze the effects of imperfect channel state information (CSI) on the outage performance of linear zero-forcing (ZF) receiver in time-varying multiple-input multiple-output (MIMO) fading channels. Accurate CSI is an essential condition to improve the overall performance of the rate-adaptive MIMO system. However, acquiring perfect CSI at transceivers is impossible due to feedback delay and channel estimation error. To investigate imperfect CSI environments, therefore, the outage probability is approximated by deriving the probability density function of the output signal-to-noise ratio (SNR) of the ZF receiver, based on temporal MIMO channel correlation. Since the exact distribution of the ZF-output SNR is yet unknown, we apply a Gaussian approximation to obtain mathematical expressions for the outage probability with the assumption of a square MIMO channel. Simulation results shows that our approximation is close to the actual outage probability.

In this paper, we propose an ensemble learning algorithm, which we call the observational learning algorithm (OLA), motivated from the observational learning theory suggested by Bandura (1971). According to the theory, in a group of children who have different and insufficient knowledge for a task, each child can lean how to do the task by observing other children. In the OLA, a neural network ensemble is regarded as a group of children. Each network is trained with the virtual data that are generated from observing other networks as well as the bootstrapping data from the original data set. The virtual data function as both temporal hints having the auxiliary information about the target function and a regularization penalty for making networks smooth. From numerical experiments involving both regression and classification problems, the OLA is shown to give better generalization performance than simple committee and bagging approaches when insufficient and noisy data are given.