Block-code based probabilistic amplitude shaping (BC-PAS) replaces the distribution matcher (DM) in the original PAS scheme by utilizing a block code decoder. In the original paper of BC-PAS, Matsumine etc. showed that BC-PAS achieves significantly reduced storage and computational complexity than DM-based PAS (DM-PAS) at the receiver. However, BC-PAS can only support spectral efficiency (SE) η within the range η≥m−1 when employing a 2m-ary pulse-amplitude modulation (2m-PAM), where m denotes the modulation order. To address this limitation, we propose a partial shaping on the BC-PAS scheme that supports SE η in the extended range ηm-PAM is used.

A novel rate-profiling design is proposed for polarization-adjusted convolutional (PAC) codes under list decoding, adopting a path probability perspective. Inspired by the concepts of Hamming distance and Hamming weight, the concepts of path probability distance (PPD) and path probability weight (PPW) are innovatively introduced to measure the disparity between the erroneous paths and the correct path for PAC codes under probabilistic decoding. An in-depth analysis of the recursion of node log-likelihood ratios (LLRs) in the factor graph is conducted, elucidating the derivation of a lower bound on the PPW as a consequential outcome. Utilizing the concept of the PPW, a rate-profiling design algorithm is proposed to establish the reliability ranking for the bit-channels of PAC codes. Simulation results demonstrate that PAC codes employing the proposed rate-profiling exhibit advantages over alternative rate-profiling and other state-of-the-art polar coding schemes across various block lengths and code rates under short decoding list sizes.

As an important part of beyond the fifth-generation (B5G) and the sixth-generation (6G) mobile communication systems, ultra-reliable and low latency communications (uRLLC) puts forward strict requirements for delay and reliability (e.g., 99.9999% reliability and$500 \mu \text{s}$latency). At present, the evaluation measures of delay and reliability are usually based on infinite block length and rely on long-term statistics, which cannot meet the requirement of low latency. The cell-free system, with a very large number of distributed antennas, has the characteristics of macro-diversity and spatial sparsity, which can further enhance the performance of uRLLC. In this paper, the downlink multidevice cell-free system with hard deadlines is considered and analyzed in the finite block length (FBL) regime. The communication’s delay and reliability are described based on two instantaneous evaluation measures: transmission error (TE) and time overflow (TO) probability. From the perspective of information theory, this paper analyzes the analytic expression of TE probability for a single device and the performance impact of FBL on the traditional channel capacity analysis. Considering the multidevice TO probability in a cell-free system, the closed-form expressions of upper and lower bounds are derived and compared with the gamma approximation results. This paper further provides three methods, namely, transmission rate selection, device grouping and space division multiplexing, to balance the delay and reliability of the system and analyzes the performance.

In this paper, we combine regular amplitude phase-shift keying (RAPSK) constellation with Gray mapping for link-level performance improvement. Under the criteria of the bit-interleaved coded modulation (BICM) mutual information (MI), we search for optimal Gray-mapped RAPSK (Gray-RAPSK) constellation with a given size. We design the labeling for Gray-RAPSK constellation based on bit-level MI. Simulation results show that shaping gains more than 0.5 dB are obtained for the 256-ary Gray-RAPSK constellation at the block error rate (BLER) of 10−2in the high spectral efficiency region. In addition, simulation results show that the error floor of low-density parity-check (LDPC) coding combined with Gray-RAPSK constellation is lower than that with quadrature amplitude modulation (QAM) constellation.

This paper studies a large random matrix system (LRMS) model involving an arbitrary signal distribution and forward error control (FEC) coding. We establish an area property based on the approximate message passing (AMP) algorithm. Under the assumption that the state evolution for AMP is correct for the coded system, the achievable rate of AMP is analyzed. We prove that AMP achieves the constrained capacity of the LRMS with an arbitrary signal distribution provided that a matching condition is satisfied. We provide related numerical results of binary signaling using irregular low-density parity-check (LDPC) codes. We show that the optimized codes demonstrate significantly better performance over unmatched ones under AMP. For quadrature phase shift keying (QPSK) modulation, bit error rate (BER) performance within 1 dB from the constrained capacity limit is observed.

Due to the limited number of traditional orthogonal pilots, pilot collision will severely degrade the performance of contention-based grant-free transmission. To alleviate the pilot collision and exploit the spatial degree of freedom as much as possible, an extremely sparse orthogonal pilot scheme is proposed for uplink grant-free transmission. The proposed sparse pilot is used to perform active user detection and estimate the spatial channel. Then, inter-user interference suppression is performed by spatially combining the received data symbols using the estimated spatial channel. After that, the estimation and compensation of wireless channel and time/frequency offset are performed utilizing the geometric characteristics of combined data symbols. The task of pilot is much lightened, so that the extremely sparse orthogonal pilot can occupy minimized resources, and the number of orthogonal pilots can be increased significantly, which greatly reduces the probability of pilot collision. The numerical results show that the proposed extremely sparse orthogonal pilot scheme significantly improves the performance in high-overloading grant-free scenario.

This paper studies a large random matrix system (LRMS) model involving an arbitrary signal distribution and forward error control (FEC) coding. We establish an area property based on the approximate message passing (AMP) algorithm. Under the assumption that the state evolution for AMP is correct for the coded system, the achievable rate of AMP is analyzed. We prove that AMP achieves the constrained capacity of the LRMS with an arbitrary signal distribution provided that a matching condition is satisfied. As a byproduct, we provide an alternative derivation for the constraint capacity of an LRMS using a proved property of AMP. We discuss realization techniques for the matching principle of binary signaling using irregular low-density parity-check (LDPC) codes and provide related numerical results. We show that the optimized codes demonstrate significantly better performance over un-matched ones under AMP. For quadrature phase shift keying (QPSK) modulation, bit error rate (BER) performance within 1 dB from the constrained capacity limit is observed.

This paper considers a compressed-coding scheme that combines compressed sensing with forward error control coding. Approximate message passing (AMP) is used to decode the message. Based on the state evolution analysis of AMP, we derive the performance limit of compressed-coding. We show that compressed-coding can approach Gaussian capacity at a very low compression ratio. Further, the results are extended to systems involving non-linear effects such as clipping. We show that the capacity approaching property can still be maintained when generalized AMP is used to decode the message. To approach the capacity, a low-rate underlying code should be designed according to the curve matching principle, which is complicated in practice. Instead, analog spatial-coupling is used to avoid sophisticated low-rate code design.

In this paper, we propose two multi-bit feedback methods for hybrid automatic repeat request (HARQ). Both methods take into consideration of the coding gain of the forward error-correction codes. One method only considers the coding gain of the first transmission, which is named accumulated power (ACP) method. The other method considers the coding gain of both the first transmission and retransmissions, which is named accumulated error-correction performance (ACEP). Simulation results show that both methods achieve higher spectral efficiency and lower latency comparing with existed methods.

This paper considers a compressed-coding scheme that combines compressed sensing with forward error control coding. Approximate message passing (AMP) is used to decode the message. Based on the state evolution analysis of AMP, we derive the performance limit of compressed-coding. We show that compressed-coding can approach Gaussian capacity at a very low compression ratio. Further, the results are extended to systems involving non-linear effects such as clipping. We show that the capacity approaching property can still be maintained when generalized AMP is used to decode the message. To approach the capacity, a low-rate underlying code should be designed according to the curve matching principle, which is complicated in practice. Instead, analog spatial-coupling is used to avoid sophisticated low-rate code design. In the end, we study the coupled scheme in a multiuser environment, where analog spatial-coupling can be realized in a distributive way. The overall block length can be shared by many users, which reduces block length per-user.

We establish a multiuser extrinsic information transfer (EXIT) chart area theorem for the interleave-division multiple access (IDMA) scheme, a special form of superposition coding, in multiple access channels (MACs). A low-cost multi-user detection (MUD) based on the Gaussian approximation (GA) is assumed. The evolution of mean-square errors (MSE) of the GA-based MUD during iterative processing is studied. We show that the K-dimensional tuples formed by the MSEs of K users constitute a conservative vector field. The achievable rate is a potential function of this conservative field, so it is the integral along any path in the field with value of the achievable rate solely determined by the two path terminals. Optimized error correcting codes can be found given the integration paths in the MSE fields by matching EXIT type functions. The above findings imply that i) low-cost GA detection can provide MAC capacity-approaching performance, ii) the sum-rate capacity can be achieved independently of the integration path in the MSE fields; and iii) the integration path determining achievable rate tuples of all users can be an extra degree of freedom for code design.

We establish a multi-user extrinsic information transfer (EXIT) chart area theorem for the interleave-division multiple-access (IDMA) scheme, a special form of superposition coding, in multiple access channels (MACs). A low-cost multi-user detection (MUD) based on the Gaussian approximation (GA) is assumed. The evolution of mean-square errors (MSE) of the GA-based MUD during iterative processing is studied. We show that the K-dimensional tuples formed by the MSEs of K users constitute a conservative vector field. The achievable rate is a potential function of this conservative field, so it is the integral along any path in the field with value of the integral solely determined by the two path terminals. Optimized codes can be found given the integration paths in the MSE fields by matching EXIT type functions. The above findings imply that i) low-cost GA-based MUD can provide near capacity performance; ii) the sum-rate capacity (region) can be achieved independently of the integration path in the MSE fields; and iii) the integration path can be an extra degree of freedom for code design.

This paper is concerned with pilot transmission schemes in a large antenna system with non-orthogonal multiple-access (NOMA). We investigate two pilot structures-orthogonal pilot (OP) and superimposed pilot (SP). In OP, pilots occupy dedicated time (or frequency) slots, while in SP, pilots are superimposed with data. We study an iterative data-aided channel estimation (IDACE) receiver, where partially decoded data are used to refine channel estimation. We analyze the achievable rates for systems with IDACE receivers for both OP and SP. We show that the optimal portion of pilot power tends to zero for SP with Gaussian signaling. This result is consistent with existing findings obtained via the replica method in statistical physics. The latter involves multiple codes, which is convenient for theoretical analysis but difficult to implement. As a comparison, IDACE is potentially implementable in practice. We demonstrate that, with code optimization, SP can outperform OP in a high mobility environment with a large number of users. We provide numerical examples to verify our analysis.

In this paper, we propose a simple procedure to construct (decodable) good codes with any given alphabet (of moderate size) for any given (rational) code rate to achieve any given target error performance (of interest) over additive white Gaussian noise channels. We start with constructing codes over groups for any given code rates. This can be done in an extremely simple way if we ignore the error performance requirement for the time being. Actually, this can be satisfied by repetition (R) codes and uncoded (UN) transmission along with time-sharing technique. The resulting codes are simply referred to as RUN codes for convenience. The encoding/decoding algorithms for RUN codes are almost trivial. In addition, the performance can be easily analyzed. It is not difficult to imagine that the RUN code usually performs far away from the corresponding Shannon limit. Fortunately, the performance can be improved as required by spatially coupling the RUN codes via block Markov superposition transmission (BMST), resulting in the BMST-RUN codes. Simulation results show that the BMST-RUN codes perform well (within around 1 dB away from Shannon limits) for a wide range of code rates and outperform the BMST with bit-interleaved coded modulation scheme.

This paper is concerned with the spatial modulation (SM), a multiple-input multiple-output (MIMO) transmission technique, that maps information bits not only into the conventional two-dimensional signal points but also into the indices of active transmit antennas. We present a two-layer coded SM scheme, in which the spatial bits carried by the antenna indices and the signal bits carried by the conventional signals are protected separately by two error correction codes. For the ease of decoding process, the code rates are allocated according to the chain rule of the mutual information. We choose block Markov superposition transmission (BMST) codes for each layer, since they are easily designed for any given code rate with a predictable performance lower bound. An iterative sliding-window decoding algorithm is also presented by exchanging messages iteratively between the two BMST decoders and the soft-in soft-out (SISO) demapper of the SM. To reduce the computational complexity, we propose to implement the SISO demapping algorithm by employing only partial soft inputs. Numerical results show that the BMST-SM system performs well over uncorrelated Rayleigh fading channels.

In this study, the authors’ present a scheme, denoted as BMST‐MSK, which combines the block Markov superposition transmission (BMST) with the minimum shift keying (MSK) signalling. The BMST‐MSK can be implemented in two forms – the BMST with recursive MSK (BMST‐RMSK) and the BMST with non‐recursive MSK (BMST‐NRMSK). The BMST‐MSK admits a sliding‐window decoding/demodulation algorithm, where two schedules with or without iterative processing between the BMST and MSK (referred to as outer iteration) are discussed. To analyse the asymptotic performance of BMST‐MSK, the authors’ first assume a genie‐aided decoder and then derive the union bound for the equivalent genie‐aided system. Numerical results show that the performances of the BMST‐MSK match well with the derived lower bounds in the low error rate regions. From simulations, the authors’ found that the outer iterations can provide performance improvement for the BMST‐RMSK, but not for the BMST‐NRMSK. Taking a (2,1,2) convolutional code with input length of 10 000 bits as the basic code, the BMST‐NRMSK achieves a bit‐error‐rate of 10 −5 at E b / N 0 = 0.45 dB over additive white Gaussian noise channels, which is away from the Shannon limit about 0.25 dB.

In this study, an efficient decoding algorithm is proposed to decode non‐binary low‐density parity‐check (LDPC) codes. The algorithm is derived from the belief‐propagation (BP) decoding with genetic algorithm of binary LDPC codes. For the proposed algorithm, two decoding constraints are introduced to determine variable nodes which are considered highly reliable. The messages from these highly reliable variable nodes are then magnified with an appropriate parameter γ . This process can make the messages propagate in the Tanner graph more efficiently. Simulation results show that, compared with the fast Fourier transform‐based BP algorithm, the proposed algorithm can have an equal or better performance in low bit‐error‐rate region over both the additive white Gaussian noise channels and the mobile fading channels.

A construction of big convolutional codes from short codes called block Markov superposition transmission (BMST) is proposed. The BMST is very similar to superposition block Markov encoding (SBME), which has been widely used to prove multiuser coding theorems. The BMST codes can also be viewed as a class of spatially coupled codes, where the generator matrices of the involved short codes (referred to as basic codes) are coupled. The encoding process of BMST can be as fast as that of the basic code, while the decoding process can be implemented as an iterative sliding-window decoding algorithm with a tunable delay. More importantly, the performance of BMST can be simply lower bounded in terms of the transmission memory given that the performance of the short code is available. Numerical results show that: 1) the lower bounds can be matched with a moderate decoding delay in the low bit-error-rate (BER) region, implying that the iterative sliding-window decoding algorithm is near optimal; 2) BMST with repetition codes and single parity-check codes can approach the Shannon limit within 0.5 dB at the BER of 10-5for a wide range of code rates; and 3) BMST can also be applied to nonlinear codes.

In this study, the authors consider designing low‐density parity‐check (LDPC) coded modulation systems to achieve unequal error protection (UEP). They propose a new UEP approach by partial superposition transmission (PST) called UEP‐by‐PST. In the UEP‐by‐PST system, the information sequence is distinguished as two parts, the more important data (MID) and the less important data (LID), both of which are coded with LDPC codes. The codeword that corresponds to the MID is superimposed on the codeword that corresponds to the LID. The system performance can be analysed by using discretised density evolution. Also proposed in this study is a criterion from a practical point of view to compare the efficiencies of different UEP approaches. Numerical results show that, over both additive white Gaussian noise channels and uncorrelated Rayleigh fading channels, (i) UEP‐by‐PST provides higher coding gain for the MID compared with the traditional equal error protection approach, but with negligible performance loss for the LID; and (ii) UEP‐by‐PST is more efficient with the proposed practical criterion than the UEP approach in the digital video broadcasting system.

For any given short code (referred to as the basic code), block Markov superposition transmission (BMST) provides a simple way to obtain predictable extra coding gain by spatially coupling the generator matrix of the basic code. This paper presents a systematic design methodology for BMST systems to approach the channel capacity at any given target bit error rate (BER) of interest. To simplify the design, we choose the basic code as the Cartesian product of a short block code. The encoding memory is then inferred from the genie-aided lower bound according to the performance gap of the short block code to the corresponding Shannon limit at the target BER. In addition to the sliding-window decoding algorithm, we propose to perform one more phase decoding to remove residual (rare) errors. A new technique that assumes a noisy genie is proposed to upper bound the performance. Under some mild assumptions, these genie-aided bounds can be used to predict the performance of the proposed two-phase decoding algorithm in the extremely low BER region. Using the Cartesian product of a repetition code as the basic code, we construct a BMST system with an encoding memory 30 whose performance at the BER of 10-15can be predicted within 1 dB away from the Shannon limit over the binary-input additive white Gaussian noise channel.

In this paper, we present a new approach, called block Markov superposition transmission (BMST), to construct from short codes a class of convolutional codes with large constraint length. The BMST is very similar to superposition block Markov encoding (SBME), which has been widely used to prove multiuser coding theorems. We also present an iterative sliding-window decoding algorithm for the proposed transmission scheme. The extra coding gain obtained by BMST can be bounded in terms of the Markov order and with the help of the input-output weight enumerating function (IOWEF) of the BMST system, which can be computed from that of the short code by performing a trellis-based algorithm. Numerical results verify our analysis and show that an extra coding gain of 6.4 dB at bit-error rate (BER) 10-5can be obtained by BMST of the [7, 4] Hamming code.