We propose a new class of high-rate spatially coupled LDPC (SC-LDPC) codes based on the convolutional selforthogonal codes (CSOCs) first introduced by Massey. The SCLDPC codes are constructed by treating the irregular graph corresponding to the parity-check matrix of a systematic rate$R=(n-1) / n$CSOC as a convolutional protograph. The protograph can then be lifted using permutation matrices to generate a high-rate SC-LDPC code whose strength depends on the lifting factor. The SC-LDPC codes constructed in this fashion can be decoded using iterative belief propagation based sliding window decoding. To improve performance, a non-systematic version of a C SOC parity-check matrix is then proposed by making a slight modification to the systematic construction. Even though the parity-check matrix is in non-systematic form, we show how systematic encoding can still be performed. We also show that the non-systematic convolutional protograph has a guaranteed girth and free distance and that these properties carry over to the lifted versions. Numerical results are included demonstrating that CSOC-based SC-LDPC codes (i) have performance at least as good as that of SC-LDPC codes commonly found in the literature, and (ii) have iterative decoding thresholds comparable to those of existing SC-LDPC code designs.

Conventional construction of non-binary polar codes divides the synthesized channels into the frozen channels and information channels. Each information channel carries one symbol i.e.$q$bits. However, there are many middle channels with insufficient polarization, which can not carry one symbol of$q$bits but only$i$bits,$1 \leq i

In this paper, we examine variable node (VN) doping to mitigate the error propagation problem in sliding window decoding (SWD) of spatially coupled LDPC (SC-LDPC) codes from the point of view of the encoding process. More specifically, in order to simplify the process of generating an encoded sequence with some number of doped code bits, we propose to employ systematic encoding and to limit doping to systematic bits only. Numerical results show that doping of systematic bits only achieves comparable performance to employing general (nonsystematic) encoding and full doping of all the code bits at each doping position, while benefiting from a much simpler encoding process. We then show that the inherent rate loss due to doping can be reduced by doping only a fraction of the variable nodes at each doping position with only a minor impact on performance.

We introduce a novel design of spatially coupled low density parity check codes in order to reduce the effects of error propagation in low-latency sliding window decoding for large frame lengths or streaming applications. Specifically, we employ reduced-degree check nodes spaced throughout the coupling chain, which have the effect of allowing the decoder to recover from error bursts. A simplified analysis of the block error rate (BLER) of the proposed codes is presented that allows us to predict the effect of different placements of reduced-degree checks in the coupling chain. Simulation results supporting the beneficial effect of the new code design on the overall BLER performance are included.

In this paper, we present an improved belief propagation list (BPL) decoding algorithm for polar codes. Rather than getting L factor graphs (FGs) at random and cyclic shift permutation, we use the upper bounds on the block error propability of polar codes with different FGs as the metric to choose the best L FGs. By observing the bounds of different FGs, we propose a heuristic method to reduce search complexity. Simulation results show that there is only a gap of 0.2 dB between the frame error rate (FER) performance of the improved BPL decoder using RM16-GA construction and that of length-1024 5G polar code decoded by SCL with the same list size of 32 at FER =10-4. Moreover, with the proposed FG selection method, BPL decoding can reduce clock cycles by 97.74% compared with the SCL decoding.

In this paper, we study the problem of error propagation in sliding window decoding (SWD) of spatially coupled LDPC (SC-LDPC) codes. A general decoder model that accounts for error propagation is proposed and analyzed, and the decoded block error rate (BLER) is calculated using the model. In order to improve the BLER performance under decoder error propagation conditions, adaptive variable node (VN) doping is proposed, assuming a noiseless binary feedback channel is available. Example calculations using the proposed model, as well as numerical simulation results, are used to show that adaptive VN doping improves the BLER performance compared to the periodic VN doping and to the undoped case.

A novel low-density parity-check (LDPC) coded Gaussian minimum shift keying (GMSK) scheme is proposed for wireless communications subject to low SNRs, limited power and spectrum resources. We first design a non-recursive GMSK modulator to alleviate the impact of error propagation. Then, a pilot-aided quasi-coherent demodulation algorithm (PA-QCDA) is derived, where a modified BCJR-based detection is used to produce the soft-output with initial and ending trellis-states being determined using the overhead-limited pilot. We choose proper parameters for the non-recursive GMSK signaling according to the trade-off of the power and spectral efficiency. Simulation results show that the proposed non-recursive GMSK system with the PA-QCDA can achieve performance similar to the LDPC coded BPSK system and can also work well in the presence of large frequency and phase offsets or burst errors.

We investigate error propagation in sliding window decoding of braided convolutional codes (BCCs). Previous studies of BCCs have focused on iterative decoding thresholds, minimum distance properties, and their bit error rate (BER) performance at small to moderate frame length. Here, we consider a sliding window decoder in the context of large frame length or one that continuously outputs blocks in a streaming fashion. In this case, decoder error propagation, due to the feedback inherent in BCCs, can be a serious problem. To mitigate the effects of error propagation, we propose several schemes: a window extension algorithm where the decoder window size can be extended adaptively, a resynchronization mechanism where we reset the encoder to the initial state, and a retransmission strategy where erroneously decoded blocks are retransmitted. In addition, we introduce a soft BER stopping rule to reduce computational complexity, and the tradeoff between performance and complexity is examined. Simulation results show that, using the proposed window extension algorithm, resynchronization mechanism, and retransmission strategy, the BER performance of BCCs can be improved by up to four orders of magnitude in the signal-to-noise ratio operating range of interest, and the soft BER stopping rule can be employed to reduce computational complexity.

In this paper, we consider the sparse code multiple access (SCMA) for low earth orbit (LEO) satellite communications to achieve high user capacity and provide technical support for satellite-based Internet of Things (IoT) applications. Note that Doppler shift in the LEO satellite link can not be ignored and the message passing algorithm (MPA) extensively utilized by SCMA is quite time-consuming due to high complexity. Thus we propose a coherent iterative receiver with low complexity for SCMA-based LEO satellite communication systems. First, we design a data-aided carrier synchronization scheme using multiple disjoint pilot blocks to estimate the Doppler shift precisely. Then, a soft-out approximate message passing (SO-AMP) algorithm with linear complexity is derived from the first-order approximation of MPA based on a novel framework of SCMA mapper. Further, a damping method is introduced into the SO-AMP detector developing a damped SO-AMP (DSO- AMP) to improve the overall performance. Numerical results show that the designed receiver can achieve excellent performance close to ideal performance with no Doppler shift while maintaining low complexity.

This paper presents a new type of globally-coupled low-density parity-check (GC-LDPC) codes whose base matrix has a cyclic structure in the global part. Therefore, the resulting codes are referred to as tail-biting GC-LDPC (TB-GC-LDPC) codes. We propose two methods to construct TB GC quasi-cyclic LDPC (TB-GC-QC-LDPC) codes. For the first method, we extract a replicated version of a constructed base matrix and mask it with a designed masking matrix. Compared to the conventional construction methods, this method provides more flexibility in code length for TB-GC-QC-LDPC codes. The second method is based on designing the incidence matrix of a special type of packings. Examples show that the constructed TB-GC-QC-LDPC codes perform well over the additive white Gaussian noise channel (AWGNC) and the binary erasure channel (BEC). The asymptotic performance of TB-GC-LDPC ensembles over BECs are also analyzed by resorting to density evolution. Moreover, numerical results show that TB-GC-LDPC ensembles can achieve better flooding-schedule decoding (FSD) thresholds than the corresponding GC-LDPC ensembles with a similar structure. With sufficient decoding iterations in the global phase, the local/global two-phase iterative decoding (TPD) thresholds of the TB-GC-LDPC ensembles significantly outperform those of the corresponding GC-LDPC ensembles as well.

In this paper, we study sliding window decoding of braided convolutional codes (BCCs) in the context of a streaming application, where decoder error propagation can be a serious problem. A window extension algorithm and a resynchronization mechanism are introduced to mitigate the effect of error propagation. In addition, we introduce a soft bit-error-rate stopping rule to reduce computational complexity, and the tradeoff between performance and complexity is examined. Simulation results show that, using the proposed window extension algorithm and resynchronization mechanism, the error performance of BCCs can be improved by up to three orders of magnitude with reduced computational complexity.

In this paper we consider the generalization of binary non-uniformly coupled low-density parity-check (LDPC) codes to that over Galois field GF (2m). We will perform an iterative decoding threshold analysis for this class of non-uniformly coupled LDPC ensembles formed by randomly coupled and protograph-based coupled ensembles, respectively. By optimizing the coupling among spatial positions, we can construct codes having excellent thresholds and small rate-loss. Moreover, we propose a list-aided windowed decoding (list-aided WD) scheme for nonbinary SC-LDPC codes with low decoding latency. Numerical results show that the list-aided WD which outperforms conventional WD can perform better performance and lower decoding latency than the flooding-schedule decoding at low SNRs on the additive white Gaussian noise channel.

Sparse code multiple access (SCMA) is a promising technique to meet the requirements for massive capacity in 5G communications. In this paper, a nonbinary LDPC- coded SCMA system with a turbo receiver is proposed. We also provide a heuristic approach based on Cartesian product and Euclidean distance to construct the SCMA codebook, which greatly reduces the detection complexity and can be easily extended to large-size constellations. Furthermore, the codebook design for large SCMA systems is presented, and the sparse structure is optimized via the construction of matrices with optimized cycle distribution. Simulation results show that the nonbinary LDPC-coded SCMA system is much more compatible with high-order modulation than its binary counterpart, and the proposed design outperforms the original SCMA codebook design in both the error probability and complexity even in large loading situations.

In this paper, we present a novel sliding window decoding scheme based on iterative Bahl-Cocke-Jelinek-Raviv decoding for braided convolutional codes, a class of turbo-like codes with short constraint length component convolutional codes. The tradeoff between performance and decoding latency is examined and, to reduce decoding complexity, both uniform and nonuniform message passing schedules within the decoding window, along with early stopping rules, are proposed. We also perform a density evolution analysis of sliding window decoding to guide the selection of the window size and message passing schedule. Periodic puncturing is employed to obtain rate-compatible code rates of 1/2 and 2/3 starting from a rate 1/3 mother code and a code rate of 3/4 starting from a rate 1/2 mother code. Simulation results show that, with nonuniform message passing and periodic puncturing, near capacity performance can be maintained throughout a wide range of rates with reasonable decoding complexity and no visible error floors.

This paper studies an extension and improvement of the joint detection-decoding algorithm for nonbinary LDPC-coded modulation systems. The iterative joint detection-decoding (IJDD) algorithm in [1] combines nonbinary LDPC decoding with signal detection based on the hard-message passing strategy, resulting in significantly reduced decoding complexity. However, it applies only to majority-logic decodable nonbinary LDPC codes with high column weight. For nonbinary LDPC codes with low column weight, a noticeable performance loss will be incurred. To handle this problem, we propose a reliability-based iterative joint detection-decoding (also termed improved IJDD) algorithm, which combines the accumulated reliability of symbols based on the one-step majority-logic decoding (MLGD) algorithm and a Chase-like local list decoding algorithm. Simulation results show that the improved IJDD algorithm outperforms the IJDD algorithm by about 0.3 dB using nonbinary LDPC codes with high column weight, and by about 3 dB using nonbinary LDPC codes with low column weight (dv= 4), while maintaining the low complexity of decoding. Compared to the FFT-QSPA, the proposed algorithm has a performance degradation of 0.5 dB in the high column weight regime, and about 1 dB in the low column weight regime.

Kite codes are a class of rateless FEC codes designed for the noisy channel. In this paper, we propose a new ensemble of nonbinary rate-compatible (RC) LDPC codes, which is constructed based on Kite codes. The proposed nonbinary RC codes (nonbinary Kite codes, for simplicity) possess coding rate varying “continuously” from 0.3 to 0.9. Moreover, the degree distribution varies with the incremental redundancy. Simulation results show that the nonbinary Kite codes outperform their binary counterparts with the BPSK modulation in a wide range of coding rates over the AWGN channel. We also examine the application of nonbinary Kite codes to fountain communications. Numerical results show that the average throughput achievable with nonbinary Kite codes can be close to the capacity within a wide region of SNRs.

In this paper, we apply the precoding technique developed by Abbasfar et al. for ARA codes to the original rate-compatible LDPC codes introduced in [1] to obtain an improved ensemble of variable-rate LDPC codes, which perform universally well over the AWGN channel in the low to high code-rate region. The proposed codes will be named precoded Kite codes. The Extrinsic Information Transfer (EXIT) chart is used to optimize the code performance. Numerical results show that the precoded Kite codes can achieve a coding gain of up to 0.3 dB over the codes in [1]. A performance comparison is also made between the proposed codes and the Raptor codes over the AWGN channel. It is shown that the proposed codes outperform the Raptor codes universally in a wide code rate range over AWGN channels. Extensive simulation results confirm that precoded Kite codes perform close to capacity within a range of code rates from 0.1 to 0.9.