Message-passing Decoding Research Articles

A Threshold-Based Binary Message Passing Decoder With Memory for Product Codes

A Threshold-Based Binary Message Passing Decoder With Memory for Product Codes

Check-Agnosia based Post-Processor for Message-Passing Decoding of Quantum LDPC Codes

The inherent degeneracy of quantum low-density parity-check codes poses a challenge to their decoding, as it significantly degrades the error-correction performance of classical message-passing decoders. To improve their performance, a post-processing algorithm is usually employed. To narrow the gap between algorithmic solutions and hardware limitations, we introduce a new post-processing algorithm with a hardware-friendly orientation, providing error correction performance competitive to the state-of-the-art techniques. The proposed post-processing, referred to as check-agnosia, is inspired by stabilizer-inactivation, while considerably reducing the required hardware resources, and providing enough flexibility to allow different message-passing schedules and hardware architectures. We carry out a detailed analysis for a set of Pareto architectures with different tradeoffs between latency and power consumption, derived from the results of implemented designs on an FPGA board. We show that latency values close to one microsecond can be obtained on the FPGA board, and provide evidence that much lower latency values can be obtained for ASIC implementations. In the process, we also demonstrate the practical implications of the recently introduced t-covering layers and random-order layered scheduling.

Two-Phase Unsourced Random Access in Massive MIMO: Performance Analysis and Approximate Message Passing Decoder

Two-Phase Unsourced Random Access in Massive MIMO: Performance Analysis and Approximate Message Passing Decoder

Tanner-Graph-Based Massive Multiple Access—Transmission and Decoding Schemes

In this paper we consider two Tanner-graph-based transmission schemes for massive multiple access, which combine non-orthogonal multiple access (NOMA) and grant-based random access. Each user transmits two data streams repeatedly using several channel time-frequency resource blocks (RBs) and the transmission schedule is represented by a Tanner graph, where variable nodes and check nodes represent the transmitted signals and the RBs, respectively. In Scheme 1 each variable node represents a data stream of a user, whereas Scheme 2 employs rate splitting and each variable node represents the superimposed data streams of a user. On the receiver side, we first consider peeling decoders that serve both as pilot-based channel estimators and baseline decoders. We then develop message-passing decoders for both transmission schemes that can fully exploit the diversity afforded by the repetitive transmission across different RBs, as opposed to the peeling decoders. We also propose a neural decoder by deep unfolding the message-passing decoder and further performing a small number of training epochs using the pilots. Simulation results show that for Transmission Scheme 1, the message-passing decoder offers decoding performance improvement over the peeling decoder by orders of magnitude; and as a result, Scheme 1 substantially outperforms Scheme 2. Moreover, the neural decoder further improves upon the performance of the message-passing decoder, as more information is learned about the transmitted data over the training epochs.

A Grant-Based Random Access Scheme With Low Latency for mMTC in IoT Networks

The design of transmission schemes and receiver techniques with high reliability and low latency for the massive machine-type communications (mMTC) is an important challenge for the future Internet of Things (IoT) systems in the sixth-generation (6G) wireless communication networks. In this paper, we propose a new physical-layer transceiver scheme for mMTC, where users transmit their data based on a pre-designed sparse Tanner graph, and the base station (BS) employs blind channel estimation and message-passing decoding to decode user data. In particular, low latency is achieved by the construction of the transmission Tanner graph, as well as a hybrid modulation scheme that consists of BPSK symbols to facilitate blind channel estimation, and general M-ary modulation to reduce the transmission delay. Moreover, high reliability is achieved by the proposed message-passing decoder that fully exploits the diversity of the transmitted signal and offers soft demodulation and decoding capabilities. We provide both performance analyses based on density evolution, and simulation results, to demonstrate the superior performance of the proposed physical-layer transceiver solution for mMTC.

Optimizing quasi-cyclic spatially coupled LDPC codes by eliminating harmful objects

It is well known that some harmful objects in the Tanner graph of low-density parity-check (LDPC) codes have a negative impact on their error correction performance under iterative message-passing decoding. Depending on the channel and the decoding algorithm, these harmful objects are different in nature and can be stopping sets, trapping sets, absorbing sets, or pseudocodewords. Differently from LDPC block codes, the design of spatially coupled LDPC codes must take into account the semi-infinite nature of the code, while still reducing the number of harmful objects as much as possible. We propose a general procedure, based on edge spreading, enabling the design of good quasi-cyclic spatially coupled LDPC (QC-SC-LDPC) codes. These codes are derived from quasi-cyclic LDPC (QC-LDPC) block codes and contain a considerably reduced number of harmful objects with respect to the original QC-LDPC block codes. We use an efficient way of enumerating harmful objects in QC-SC-LDPCCs to obtain a fast algorithm that spans the search space of potential candidates to select those minimizing the multiplicity of the target harmful objects. We validate the effectiveness of our method via numerical simulations, showing that the newly designed codes achieve better error rate performance than codes presented in previous literature.

266 nm ultraviolet communication under unknown interference using UVC micro-LED.

Ultraviolet C (UVC) micro light-emitting diode (LED) can achieve symbol communication rate up to 100Msps at distance 40 meters without transmitter-side lens to guarantee certain communication mobility. We consider what we believe to be a new scenario where high speed UV communciation is realized under unknown low-rate interference. The signal amplitude properties are characterized, and the interference intensity is categorized into three cases, namely weak, medium and high interference intensity. The achievable transmission rates for the three cases are derived, where the achievable transmission rate for medium interference intensity can approach those in weak interference intensity and strong interference intensity cases. We provide Gaussian approximation and related log-likelihood ratio (LLR) calculation, which are fed into the subsequent message-passing decoder. In the experiment, the data is transmitted with symbol rate 20 Msps under unknown interference with symbol rate 1 Msps, received by one photomultiplier tube (PMT). Experimental results show that the proposed interference symbol estimation approach shows negligibly higher bit error rate (BER) compared with those with perfect knowledge on the interference symbols.

A new HARQ scheme for 5G systems via interleaved superposition retransmission

Within the framework of the 5G new radio (NR), we propose a new hybrid automatic repeat request (HARQ) scheme to improve the throughput performance. The difference between the proposed scheme and the conventional one lies in the first retransmission, where the erroneous coded block group is interleaved and superimposed (XORed) onto a fresh coded block group. At the receiver, an iterative message-passing decoding algorithm can be employed to recover the target erroneous code block group (CBG). Only when the superposed retransmission fails, the conventional incremental redundancy (IR) or repetition redundancy (RR) retransmission is initiated. In any case, since the first retransmission is along with but has negligible effect on the fresh CBG, it costs neither transmitted power nor bandwidth. Monte-Carlo simulation results reveal that the presented HARQ schemes can achieve throughput improvements up to 10% over block fading channels and up to 50% over fast fading channels in comparison with the original 5G CBG-level HARQ scheme but without excessively increasing the implementation complexity.

Low-density parity-check codes: Highway to channel capacity

Low-density parity-check (LDPC) codes are not only capacity-approaching, but also greatly suitable for high-throughput implementation. Thus, they are the most popular codes for high-speed data transmission in the past two decades. Thanks to the low-density property of their parity-check matrices, the optimal maximum a posteriori probability decoding of LDPC codes can be approximated by message-passing decoding with linear complexity and highly parallel nature. Then, it reveals that the approximation has to carry on Tanner graphs without short cycles and small trapping sets. Last, it demonstrates that well-designed LDPC codes with the aid of computer simulation and asymptotic analysis tools are able to approach the channel capacity. Moreover, quasi-cyclic (QC) structure is introduced to significantly facilitate their high-throughput implementation. In fact, compared to the other capacity-approaching codes, QC-LDPC codes can provide better area-efficiency and energy-efficiency. As a result, they are widely applied in numerous communication systems, e.g., Landsat satellites, Chang'e Chinese Lunar mission, 5G mobile communications and so on. What's more, its extension to non-binary Galois fields has been adopted as the channel coding scheme for BeiDou navigation satellite system.

Sparse IDMA: A Joint Graph-Based Coding Scheme for Unsourced Random Access

This article introduces a novel communication paradigm for the unsourced, uncoordinated Gaussian multiple access problem. The major components of the envisioned framework are as follows. The encoded bits of every message are partitioned into two groups. The first portion is transmitted using a compressive sensing scheme, whereas the second set of bits is conveyed using a multi-user coding scheme. The compressive sensing portion is key in sidestepping some of the challenges posed by the unsourced aspect of the problem. The information afforded by the compressive sensing is employed to create a sparse random multi-access graph conducive to joint decoding. This construction leverages the lessons learned from traditional IDMA into creating low-complexity schemes for the unsourced setting, while also accounting for inherent randomness. Under joint message-passing decoding, the proposed scheme offers good performance at a low computational complexity. Findings are supported by numerical simulations, and results are compared to existing alternatives.

A Message Passing-Assisted Iterative Noise Cancellation Method for Clipped OTFS-BFDM Systems.

Compared with orthogonal frequency division multiplexing (OFDM) systems, orthogonal time frequency space systems based on bi-orthogonal frequency division multiplexing (OTFS-BFDM) have lower out-of-band emission (OOBE) and better robustness to high-mobility scenarios, but suffer from a higher peak-to-average ratio (PAPR) in large data packets. In this paper, one-iteration clipping and filtering (OCF) is adopted to reduce the PAPR of OTFS-BFDM signals. However, the extra noise introduced by the clipping process, i.e., clipping noise, will distort the desired signal and increase the bit error rate (BER). We propose a message passing (MP)-assisted iterative cancellation (MP-AIC) method to cancel the clipping noise based on the traditional MP decoding at the receiver, which incorporates with the (OCF) at the transmitter to keep the sparsity of the effective channel matrix. The main idea of MP-AIC is to extract the residual signal fed to the MP detector by iteratively constructing reference clipping noise at the receiver. During each iteration, the variance of residual signal and channel noise are taken as input parameters of MP decoding to improve the BER. Moreover, the convergence probability of the modulation alphabet after MP decoding in the current iteration is used as the initial probability of MP decoding in the next iteration to accelerate the convergence rate of MP decoding. Simulation results show that the proposed MP-AIC method significantly improves MP-decoding accuracy while accelerating the BER convergence in the clipped OTFS-BFDM system. In the clipped OTFS-BFDM system with rectangular pulse shaping, the BER of MP-AIC with two iterations can be reduced by 72% more than that without clipping noise cancellation.

Deep-Learning for Breaking the Trapping Sets in Low-Density Parity-Check Codes

In the low-error rate regime, message-passing (MP) decoding for low-density parity-check (LDPC) codes is known to have performance degradation due to trapping sets (TSs), which often limits the use of LDPC codes for applications with low target error rates like storage devices. This work proposes a novel deep-learning based decoding algorithm which is tailored for breaking TSs. In particular, when MP decoding fails due to TSs, there exist pairs of unsatisfied check nodes (CNs) which are connected through paths only with error variable nodes (VNs), i.e., VNs with erroneous hard-decision results. The proposed algorithm efficiently identifies the paths with error VNs between unsatisfied CNs with the aid of deep-learning techniques. Then, the decoding failures are resolved by repeating the MP decoding after re-initializing the channel outputs for the error VNs in the identified paths. In addition, by analyzing the behaviors of the deep-learning based algorithm, we propose a low-complexity algorithm, called adaptive-error-path (AEP) detector. Simulation results show that the proposed algorithms efficiently break the TSs and significantly improve the error-floor performance in the low error-rate regime.

A Deep Learning Assisted Node-Classified Redundant Decoding Algorithm for BCH Codes

This paper proposes a node-classified redundant decoding (NC-RD) algorithm based on the received sequence’s channel reliability for high-density parity-check (HDPC) codes. Two preprocessing steps are proposed prior decoding. The variable nodes of the parity-check matrix are firstly classified by the $k$ -median algorithm based on the number of shortest cycles associated with each variable node before decoding. Then, by searching among the automorphism group of the HDPC codes, we generate a list of permutations for bit positions by computing and sorting the permutation reliability metrics. The redundant decoder conducts the message-passing decoding according to the sorted permutations, which limit the unreliable information propagation for each permutation. Besides proposing a list decoding algorithm on top of the NC-RD algorithm to augment the decoder’s performance, we show that the NC-RD algorithm can be transformed into a neural network system. More specifically, multiplicative tuneable weights are attached to the decoding messages to optimize the decoding performance. Simulation results of BCH codes over the AWGN channels show that the NC-RD algorithm provides a performance gain compared to the random redundant decoding algorithm. Additional decoding performance gain can be obtained by both the list decoding method and the neural network “learned” NC-RD algorithm.

Error Floor Estimation of LDPC Decoders — A Code Independent Approach to Measuring the Harmfulness of Trapping Sets

The linear state-space model is a well-known code-independent method to estimate the contribution of a trapping set (TS) structure to the error floor of low-density parity-check (LDPC) codes. In this paper, we provide an in-depth analysis of this method by incorporating a more accurate model for the incoming messages to the TS structure that takes into account the randomness and the correlation among such messages. Based on this analysis, we demonstrate that both randomness and correlation result in the over-estimation of the failure probability of the TS. We then propose an alternate code-independent technique for the error floor estimation of iterative LDPC decoders that can accurately estimate the contribution of different TS structures in the error floor. Compared to the linear state-space model, the proposed method is not only more accurate, but also more general, in that, it is applicable to any saturating iterative message-passing decoder, symmetrically quantized or unquantized, over any memoryless binary-input output-symmetric channel. The proposed technique can be viewed as the local application of importance sampling (IS) to the message-passing algorithm over the subgraph induced by the TS in the code’s Tanner graph. In the message-passing process, to account for the effect of the rest of the Tanner graph, density evolution along with a simple correlation model is used to generate the messages coming into the TS from the rest of the Tanner graph. Extensive simulations demonstrate that the proposed technique can accurately estimate the error floor of LDPC codes over both additive white Gaussian noise (AWGN) channel and binary symmetric channel (BSC), for a variety of iterative decoding algorithms and quantization schemes.

LDPC-based Joint Source Channel Coding and Decoding Strategies for single relay cooperative communications

This paper investigates new cooperative communication strategies based on Low-Density Parity-Check codes (LDPC) with Joint Source-Channel (JSC) coding and decoding algorithms to efficiently deliver a correlated content to a destination node. The proposed strategies rely on double LDPC codes where the source and the channel coding are similar to standard LDPC operations, and can be mapped on Tanner graphs for message-passing decoding. Three coding strategies are proposed where different LDPC source and channel coding setups are applied at the source node and the relay node. For each transmission strategy, we propose a graph mapping the whole network, over which iterative message-passing decoding is applied, and where the probability of errors in the source–relay link are taken into account. We showed, based on computer simulations, that the proposed strategies can provide substantial improvements compared to equivalent rates point-to-point systems. Simulation results also showed that the system performance depends on the relay position, and that adapting the source and the relay channel coding rates accordingly can enhance the overall system performance for a time-varying network.

Coarsely Quantized Decoding and Construction of Polar Codes Using the Information Bottleneck Method

The information bottleneck method is a generic clustering framework from the field of machine learning which allows compressing an observed quantity while retaining as much of the mutual information it shares with the quantity of primary relevance as possible. The framework was recently used to design message-passing decoders for low-density parity-check codes in which all the arithmetic operations on log-likelihood ratios are replaced by table lookups of unsigned integers. This paper presents, in detail, the application of the information bottleneck method to polar codes, where the framework is used to compress the virtual bit channels defined in the code structure and show that the benefits are twofold. On the one hand, the compression restricts the output alphabet of the bit channels to a manageable size. This facilitates computing the capacities of the bit channels in order to identify the ones with larger capacities. On the other hand, the intermediate steps of the compression process can be used to replace the log-likelihood ratio computations in the decoder with table lookups of unsigned integers. Hence, a single procedure produces a polar encoder as well as its tailored, quantized decoder. Moreover, we also use a technique called message alignment to reduce the space complexity of the quantized decoder obtained using the information bottleneck framework.

Spatially-Coupled Protograph for NOMA Optimized by the Genetic Algorithm

In this paper we investigate the codebook design of the non-orthogonal multiple access through the spatially-coupled protograph. The optimization is realized by changing the edge connections in the protograph to maximize the sum rate and then permutating the identity matrices in the spatial coupling to improve the girth distribution. The edge connection in the protograph determines the interference at each resource element and the diversity for each user equipment, and the optimization finds the best tradeoff in between. The spatial coupling enlarges or removes the short girths in the protograph in favor of message-passing decoding, which makes the low-complexity detection applicable. The genetic algorithm is employed in the optimizations of both the protograph and the spatial coupling. Numerical results reveal the characteristics of the optimal superposition structures for different SNR regions and the improvement of girth distributions for different spatial coupling mechanisms. The optimized structures demonstrate better error performance than those proposed in the literature.

LDPC Code Design for Two-Layer Spatial Modulation

In Spatial Modulation (SM), the information bits are split into two streams: one is mapped to a conventional complex signal modulation, and the other is used to select the active transmit antenna. Transmission SM schemes can be implemented with a single RF chain, allowing for a low-complexity transmitterwith relatively large spectral efficient. In this paper, we are concerned with coded SM schemes. In the literature, the usual approach considers a single encoder that jointly encodes both bit streams. In this work, we propose a coded SM system in which each of the information streams is encoded by a possibly different low-density parity-check (LDPC) code. The two LDPC codes are designed after selecting the code rates according to the mutual information associated with the two corresponding subchannels, for a fixed, reference signal-to-noise ratio (SNR). A two-layer, iterative message-passing decoder is developed, where the two component decoders exchange soft information. Through Monte Carlo simulations, we show that the bit error rate of the proposed scheme is low when the SNR is greater or equal to the reference SNR, demonstrating the strength of the proposed two-layer approach.

Practical MIMO-NOMA: Low Complexity and Capacity-Approaching Solution

MIMO-NOMA combines multiple-input multiple-output (MIMO) and non-orthogonal multiple access (NOMA) techniques to address heterogeneous challenges, such as massive connectivity, low latency, and high reliability in the 5G cellular communication system and beyond. In this paper, a coded MIMO-NOMA system with capacity-approaching performance and low implementation complexity is proposed. Specifically, the proposed MIMO receiver consists of a linear minimum mean-square error (LMMSE) multi-user detector and a bank of single-user message-passing decoders, which decompose the overall NOMA signal recovery into distributed low-complexity computations with iterative processing. An asymptotic extrinsic information transfer analysis is employed to model the overall performance, and a novel class of multi-user irregular repeat-accumulate channel codes that match with the LMMSE multi-user detector in the iterative decoding process are constructed for the system. As a result, the proposed coded MIMO-NOMA system achieves asymptotic performance within 0.2 dB from the theoretical capacity. Simulation results validate the reliability and robustness of the proposed system in practical settings that include different system loads, iteration numbers, code lengths, fast/block fading, and imperfect channel estimation.

Low-Complexity Concatenated LDPC-Staircase Codes

A low-complexity soft-decision concatenated FEC scheme, consisting of an inner LDPC code and an outer staircase code is proposed. The inner code is tasked with reducing the bit error probability below the outer-code threshold. The concatenated code is obtained by optimizing the degree distribution of the inner-code ensemble to minimize estimated data-flow, for various choices of outer staircase codes. A key feature that emerges from this optimization is that it pays to leave some inner codeword bits completely uncoded, thereby greatly reducing a significant portion of the decoding complexity. The trade-off between required SNR and decoding complexity of the designed codes is characterized by a Pareto frontier. Computer simulations of the resulting codes reveals that the net coding-gains of existing designs can be achieved with up to 71\% reduction in complexity. A hardware-friendly quasi-cyclic construction is given for the inner codes, which can realize an energy-efficient decoder implementation, and even further complexity reductions via a layered message-passing decoder schedule.