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Low-density parity-check (LDPC) codes play an important role in the reliability enhancement of commercial NAND flash memory. Unfortunately, due to the requirement of the reading speed of NAND flash memory, the LDPC decoder will not obtain precise soft information to achieve high error-correcting capability. In this work, we use a density evolution (DE) algorithm to reveal the decoding threshold of the LDPC decoder affected by the read voltages. We propose the efficient design of read voltages so that the LDPC decoder has the lowest decoding threshold. Therefore, this method can guarantee that the designed read voltages are suitable for a given LDPC code. Moreover, since we found that the designed read voltages are related to the structure of the LDPC code, the joint design of the read voltages and LDPC code is then proposed to achieve the capacity of NAND flash memory. The simulation results demonstrate that our proposed design significantly improves the frame error rate (FER) performance of NAND flash memory.

Very few studies have emphasized the effects of high-pressure sintering on snow density evolution, even though snow as a type of engineering material is widely used in construction engineering in cold regions for snow pavement, snow runway and polar infrastructure. This study presents new experimental results of snow densification under high pressures of up to 100 MPa for a temperature range from −3.5 to −17.3°C and uniaxial compression at the temperature of −10°C and constant strain rates from 5 × 10−4 to 10−1 s−1. Results reveal that density evolution of snow to ice under high-pressure sintering can be achieved in a wide temperature range within a duration as short as 5 min. The compressive strength of snow-sintered ice was ~1.2–2.2 times as large as that of water-frozen ice reported by previous work. The orthogonal experiment showed that pressure is a more significant factor affecting the final density in comparison with sintering temperature and time. The increased rates of ice fabrication, low limitations on temperature and reliable sintered snow strength indicate that snow-ice engineering, such as airport construction in Greenland and Antarctica, can be improved by high-pressure sintering of snow to overcome the harsh environment.

Batched Sparse (BATS) codes are a type of network coding scheme that use a combination of random linear network coding (RLNC) and fountain coding to enhance the reliability and efficiency of data transmission. In order to achieve unequal error protection for different data, researchers have proposed unequal error protection BATS (UEP-BATS) codes. However, current UEP-BATS codes suffer from high error floors in their decoding performance, which restricts their practical applications. To address this issue, we propose a novel UEP-BATS code scheme that employs a precoding stage prior to the weighted BATS code. The proposed precoding stage utilizes a partially regular low-density parity-check (PR-LDPC) code, which helps to mitigate the high error floors in the weighted BATS code We derive the asymptotic performance of the proposed scheme based on density evolution (DE). Additionally, we propose a searching algorithm to optimize precoding degree distribution within the complexity range of the precoding stage. Simulation results show that compared to the conventional weighted BATS codes, our proposed scheme offers superior UEP performance and lower error floor, which verifies the effectiveness of our scheme. [ABSTRACT FROM AUTHOR]

Accurate prediction of noise propagation in biological networks is key to understanding faithful signal propagation in gene networks as well as for designing noise-tolerant synthetic gene circuits. Knowledge on how biological fluctuations propagate up the development ladder of biological systems is currently lacking. Similarly, little research effort has been devoted to the analysis of error propagation in biological networks. To capture and characterize error evolution, this paper considers a Boolean network (BN) model representation of a biological network such that nodes on the graph represent diverse biological entities, e.g., proteins, genes, messenger-RNAs, etc. In addition, the network edges capture the interactions between nodes. By conducting a density evolution analysis on the graphical model based on node functionalities, a recursive closed-form expression for error propagation is derived. Subsequently, the recursive equation allows us to obtain a necessary condition to guarantee noise-error elimination in dynamic discrete gene networks. Our analytical formulations provide a step toward achieving optimal network parameters for resilience against variability or noise in biology.

We design a low-density parity-check (LDPC) coded multi-user (MU) massive multiple-input multiple-output (MIMO) system with an iterative joint detection and decoding (JDD) algorithm. As a low-complexity MU detection scheme, we consider a factor graph based belief propagation detection with Gaussian approximation of interference, called a FG-GAI BP detection. We introduce a factor graph representation of LDPC coded MU massive MIMO system and define the message updating rule in the JDD process. We devise a design tool for analyzing extrinsic information transfer (EXIT) characteristics of messages exchanged in JDD, based on which degree distribution of LDPC codes and a JDD strategy are efficiently designed for coded MU massive MIMO systems. A JDD strategy and LDPC codes are designed such that a fast convergence of JDD and a low bit error probability are attained. It is observed that the coded MU massive MIMO system equipped with LDPC codes and the JDD strategy designed by the proposed method shows a lower bit error rate than conventional ones with a given number of iterations.

Bone remodelling is a complex biomechanical process, which has been studied widely based on the restrictions of local continuum theory. To provide a nonlocal bone remodelling framework, we propose, for the first time, a peridynamic formulation on the macroscale. We illustrate our implementation with a common benchmark test as well as two load cases of the proximal femur. On the one hand, results of our peridynamic model with diminishing nonlocality measure converge to the results of a local finite element model. On the other hand, increasing the neighbourhood size shows to what extent the additional degree of freedom, the nonlocality, can influence the density evolution. [ABSTRACT FROM AUTHOR]

Very few studies have emphasized the effects of high-pressure sintering on snow density evolution, even though snow as a type of engineering material is widely used in construction engineering in cold regions for snow pavement, snow runway and polar infrastructure. This study presents new experimental results of snow densification under high pressures of up to 100 MPa for a temperature range from −3.5 to −17.3°C and uniaxial compression at the temperature of −10°C and constant strain rates from 5 × 10−4 to 10−1 s−1. Results reveal that density evolution of snow to ice under high-pressure sintering can be achieved in a wide temperature range within a duration as short as 5 min. The compressive strength of snow-sintered ice was ~1.2–2.2 times as large as that of water-frozen ice reported by previous work. The orthogonal experiment showed that pressure is a more significant factor affecting the final density in comparison with sintering temperature and time. The increased rates of ice fabrication, low limitations on temperature and reliable sintered snow strength indicate that snow-ice engineering, such as airport construction in Greenland and Antarctica, can be improved by high-pressure sintering of snow to overcome the harsh environment. [ABSTRACT FROM AUTHOR]

In this paper, we derive an upper bound on load-threshold of coded slotted ALOHA (CSA) for slot erasure channel (SEC) and that for packet erasure channel (PEC), respectively. In SEC, by exploiting the analogy between Gaussian elimination of solving linear equations and the iterative successive interference-cancellation (SIC) decoding procedure of CSA, we derive the upper performance bound for SEC. Subsequently, in PEC, utilizing density evolution to track the average probability of packet-decoded failure within the SIC decoding process, we obtain the upper bound for PEC. Moreover, we propose a numerical search algorithm of these bounds under a given calculating precision. The numerical results indicate that the asymptotic upper limit on load-threshold of CSA over SEC is always less than that over PEC with any given erasure probability and average transmission rate. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel state-space model to represent the behavior of sum-product algorithm (SPA) in the vicinity of a trapping set (TS) of a low-density parity-check (LDPC) code over the additive white Gaussian noise (AWGN) channel in the error floor region. The proposed model takes into account the non-linear behavior of SPA in the initial iterations using a quadratic approximation, and dynamically adjusts the operating point of the model in accordance to the statistical properties of TS messages. This is in contrast to the existing linear state-space models which linearly approximate the non-linear behavior of SPA at around the operating point of zero in all iterations. Simulation results are provided to demonstrate the higher accuracy of the proposed model in estimating the error floor of LDPC codes compared to the linear state-space model. We also make connections to the semi-analytical code-dependent technique proposed by Richardson for the error floor estimation of LDPC codes, and demonstrate that the proposed state-space model not only is a fully-analytical code-independent counterpart to that method, but also has less complexity and, in some cases, more accuracy. [ABSTRACT FROM AUTHOR]

A new class of spatially-coupled turbo-like codes (SC-TCs), dubbed generalized spatially coupled parallel concatenated codes (GSC-PCCs), is introduced. These codes are constructed by applying spatial coupling on parallel concatenated codes (PCCs) with a fraction of information bits repeated $q$ times. GSC-PCCs can be seen as a generalization of the original spatially-coupled parallel concatenated codes proposed by Moloudi et al., 2017. To characterize the asymptotic performance of GSC-PCCs, we derive the corresponding density evolution equations and compute their decoding thresholds. The threshold saturation effect is observed and proven. Most importantly, we rigorously prove that the rate- $R$ GSC-PCC ensemble with 2-state convolutional component codes achieves at least a fraction $1-\frac {R}{R+q}$ of the capacity of the binary erasure channel (BEC) for repetition factor $q\geq 2$ and this multiplicative gap vanishes as $q$ tends to infinity. To the best of our knowledge, this is the first class of SC-TCs that are proven to be capacity-achieving. Further, the connection between the strength of the component codes, the decoding thresholds of GSC-PCCs, and the repetition factor is established. The superiority of the proposed codes with finite blocklength is exemplified by comparing their error performance with that of existing SC-TCs via computer simulations. [ABSTRACT FROM AUTHOR]

In this letter, we design and analyse analog fountain codes (AFC) for the multiple access channel (MAC). First, we present several encoding schemes, including the superposition coding and joint encoding, and decoding schemes, including successive interference cancellation and joint decoding, for multiple access AFC (MA-AFC). We propose different combinations of encoding and decoding schemes for MA-AFC and evaluate their performance in terms of block error rate (BLER) to determine which combination has the best performance. We propose a density evolution (DE) based framework to track the evolution of messages exchanged between check nodes and variable nodes in the iterative joint belief propagation (BP) decoder of MA-AFC. With the proposed DE framework, we formulate optimisation problems to find the optimal AFC code parameters, specifically the weight set, which minimises the bit error rate at a given signal-to-noise ratio (SNR). Simulation results show that the AFC code with the optimised parameters outperforms existing AFC code designs in the multiple access scenario. [ABSTRACT FROM AUTHOR]

Batched Sparse (BATS) codes are a type of network coding scheme that use a combination of random linear network coding (RLNC) and fountain coding to enhance the reliability and efficiency of data transmission. In order to achieve unequal error protection for different data, researchers have proposed unequal error protection BATS (UEP-BATS) codes. However, current UEP-BATS codes suffer from high error floors in their decoding performance, which restricts their practical applications. To address this issue, we propose a novel UEP-BATS code scheme that employs a precoding stage prior to the weighted BATS code. The proposed precoding stage utilizes a partially regular low-density parity-check (PR-LDPC) code, which helps to mitigate the high error floors in the weighted BATS code We derive the asymptotic performance of the proposed scheme based on density evolution (DE). Additionally, we propose a searching algorithm to optimize precoding degree distribution within the complexity range of the precoding stage. Simulation results show that compared to the conventional weighted BATS codes, our proposed scheme offers superior UEP performance and lower error floor, which verifies the effectiveness of our scheme.

Random access systems are potential for Internet of Things in the future wireless communication network for its operational simplicity. Irregular repetition slotted ALOHA (IRSA) system is one of the high-efficiency random access systems. In this paper, performance analysis of the irregular repetition slotted ALOHA systems with short-packet, i.e. finite-blocklength, transmission for the quasi-static Rayleigh fading channel is given. A cumulative distribution function of signal-to-interference power ratio (SIR) is derived and thus a closed-form expression of an average packet error probability (PEP) at the SIR with short packets for the Rayleigh fading channel is given. The closed-form expression makes it possible to optimize the degree distributions at a specific blocklength in the sense that the systems give the maximum system load. [ABSTRACT FROM AUTHOR]

Sliding window decoding has been employed as the decoding scheme of quasi-cyclic spatially-coupled low-density parity-check (QC-SC-LDPC) codes, with the decoding latency and complexity independent of the coupling length but proportional to the window size. The window size was empirically chosen at least three times the constraint length in previous works, which results in the preference of QC-SC-LDPC codes with small constraint length, to reduce the decoding latency and complexity in practical systems. However, the code design freedom and the decoder throughput are limited for these QC-SC-LDPC codes. In this paper, the optimal window size under the constraint of practical decoding complexity is analyzed employing multi-edge-type density evolution (MET-DE). It can be verified from the MET-DE analytical result that the optimal window size could achieve less than twice the constraint length for several edge spreading patterns, which largely loose this restriction in practical code design. Furthermore, it could be observed that besides the constraint length, the specific structure of the edge spreading pattern could affect the optimal window size as well, and thus the MET-DE analytical method for the optimal window size could effectively guide the design of QC-SC-LDPC codes in practical systems. Then an improved sliding window decoding scheme is proposed, including the optimal choice of window size and a parity-check based early termination scheme. Finally, the performance and robustness of the proposed sliding window decoding scheme for QC-SC-LDPC codes are demonstrated via simulation, with the decoding complexity at most twice as that of the conventional LDPC coded schemes. [ABSTRACT FROM AUTHOR]

We study spatially coupled LDPC codes that allow access to sub-blocks much smaller than the full code block. Sub-block access is realized by a semi-global decoder that decodes a chosen target sub-block by only accessing the target, plus a prescribed number of helper sub-blocks adjacent in the code chain. This paper develops a theoretical methodology for analyzing the semi-global decoding performance of spatially coupled LDPC codes constructed from protographs. The main result shows that semi-global decoding thresholds can be derived from certain thresholds we define for the single-sub-block graph. These characterizing thresholds are also used for deriving lower bounds on the decoder’s performance over channels with variability across sub-blocks, which are motivated by applications in data storage. [ABSTRACT FROM AUTHOR]

We propose novel sparse-graph-based transmission schemes and receiver algorithms for unsourced multiple access (UMA) in MIMO channels. The channel coherence interval is divided into a number of sub-slots and each active transmitter selects certain sub-slots to repeatedly transmit its codeword according to a sparse Tanner graph. We propose iterative receiver algorithms that at each iteration decode either a single codeword, or two or three codewords jointly, and then subtract the decoded codewords from received signals during all sub-slots. The keys to these decoders are novel blind channel estimation algorithms when the received signal contains one, two, or three codewords. We perform density evolution analysis on the proposed UMA systems to obtain the asymptotic upper bounds on the maximum achievable rates for different decoders under both regular and irregular Tanner graphs. Extensive simulation results are provided to illustrate the performance of the proposed UMA systems, and its advantages over existing compressed-sensing (CS)-based UMA schemes. [ABSTRACT FROM AUTHOR]

Uncoordinated multiple access has been proposed as a modern technique to provide massive connectivity. Among many proposals, irregular repetition slotted ALOHA (IRSA) was shown to achieve a close-to-optimum throughput by irregular packet repetition and successive interference cancellation (SIC). However, most of the previous works are based on certain ideal assumptions. In this paper, we tackle one of such ideal assumptions, where a decoded packet can always be used to cancel out all its replicas transmitted in other slots. In reality, the random nature of IRSA results in a large dynamic range of the received power that cannot be recovered under a practical quantizer. A SIC limit that dictates the number of recoverable collided packets at a slot should exist. To resolve this issue, we propose a novel protocol, named IRSA with frame partitioning (IRSA-FP), which partitions a frame into several subframes. A feedback mechanism is enforced to inform those users, whose packets have been successfully decoded, to cease their transmissions. We then propose a novel density-evolution-type analysis for IRSA-FP. Simulation results show the performance of the proposed IRSA-FP can be accurately predicted by our analysis and the proposed IRSA-FP outperforms the traditional IRSA when practical SIC limit is introduced. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Since polar codes are capacity-achieving codes, there have been various research works devoted to devising efficient implementation methods as well as improving error-correction performance. Since quantization is a critical implementation issue, in this paper, a nonuniform quantization method is proposed for the successive cancellation (SC) decoder of polar codes, which finds quantization boundary values based on the analysis of various quantization levels over the additive white Gaussian noise channel. Since low computational complexity, high reliability, and efficient memory management are required in the next-generation communication and memory systems, 2–4 bit precision levels are mainly considered in the proposed nonuniform quantization method. Depending on the presence of erasure, quantization levels are divided into three types, and the message alphabets and update rules are derived for each type. Also, a construction method of polar codes suitable for the proposed nonuniform-quantized SC decoder is proposed, which simultaneously determines the information set and the quantization boundary values based on the density evolution analysis and an upper bound of the block error probability. To determine quantization boundary values, a multivariate objective function is defined and an iterative coarse-to-fine search algorithm to minimize this objective function is proposed. In addition, a scaling method of quantizer output values is proposed when the number of quantization levels of quantizer is smaller than the number of quantization levels of decoder. Finally, simulation results confirm that the proposed nonuniform-quantized SC decoder shows better error-correction performance, lower decoding complexity, and higher memory efficiency compared to the best known uniform-quantized SC decoder.

In any transmission scheme, security against eavesdroppers is of importance. Contrary to classical encryption, security directly at the physical layer can be achieved by applying suited coding and modulation schemes. In this paper, coded modulation schemes, i.e., the use of higher-order constellations, is studied for generating both security against a wiretapper and reliability for the legitimate user. Specifically, a multilevel coding (MLC) scheme is considered. The influence of the constellation, in particular its cardinality and its dimensionality, on the gained security is assessed. As LSB component code, a practical secure coding scheme based on punctured LDPC codes is used. The security level for the employed LDPC code ensembles within MLC constructions is examined with an adapted density evolution technique. Results from numerical simulations cover the theoretical considerations and match with the derived asymptotic behavior. The results are compared to the situation when straightforwardly applying a binary code according to the BICM approach. [ABSTRACT FROM AUTHOR]

Coded Slotted ALOHA (CSA) is a random access scheme based on the application of packet erasure correcting codes to transmitted packets and the use of successive interference cancellation at the receiver. CSA has been widely studied and a common assumption is that interference cancellation can always be applied perfectly. In this paper, we study the design of CSA protocol, accounting for a non-zero probability of error due to imperfect interference cancellation (IC). A classical method to evaluate the performance of such protocols is density evolution, originating from coding theory, and that we adapt to our assumptions. Analyzing the convergence of density evolution in asymptotic conditions, we derive the optimal parameters of CSA, i.e., the set of code selection probabilities of users that maximizes the channel load. A new parameter is introduced to model the packet loss rate of the system, which is non-zero due to potential IC errors. Multi-packet reception (MPR) and the performance of 2-MPR are also studied. We investigate the trade-off between optimal load and packet loss rate, which sheds light on new optimal distributions that outperform known ones. Finally, we show that our asymptotic analytical results are consistent with simulations obtained on a finite number of slots. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the design and analysis of the Analog Fountain Code (AFC) for short packet communications. We first propose a density evolution (DE) based framework, which tracks the evolution of the probability density function of the messages exchanged between variable and check nodes of AFC in the belief propagation decoder. Using the proposed DE framework, we formulate an optimisation problem to find the optimal AFC code parameters, including the weight-set, which minimises the bit error rate at a given signal-to-noise ratio (SNR). Our results show the superiority of our AFC code design compared to existing designs of AFC in the literature and thus the validity of the proposed DE framework in the asymptotically long block length regime. We then focus on selecting the precoder to improve the performance of AFC at short block lengths. Simulation results show that lower precode rates obtain better realised rates over a wide SNR range for short information block lengths. We also discuss the complexity of the AFC decoder and propose a threshold-based decoder to reduce the complexity. [ABSTRACT FROM AUTHOR]

This paper proposes a new finite precision iterative decoder for low-density parity-check (LDPC) codes. The proposed decoder, named Sign-Preserving Min-Sum (SP-MS), significantly improves the decoding performance compared to the classical Offset Min-Sum (OMS) decoder when messages are quantized on $q=2$ , 3, or 4 bits. The particularity of the SP-MS decoder is that messages cannot take the 0 value, and can fully benefit from the $q$ bits of precision. The optimization of the SP-MS decoder is investigated in the asymptotic limit of the code length using density evolution (DE). Our study shows that 3-bit SP-MS decoders can achieve the same error-correcting performance as 5-bit OMS decoders, and 2-bit SP-MS decoders outperform 3-bit OMS decoders. The finite-length simulations confirm the conclusions of the DE analysis for several LDPC codes. Our SP-MS decoder shows a signal-to-noise ratio (SNR) gain up to 0.43 dB, with a memory/wire reduction of up to 40%, compared to the OMS decoder. Moreover, the SP-MS decoder converges faster and uses fewer iterations than the OMS decoder, with an improvement of up to 83.3% of the average decoding throughput. On an FPGA, the SP-MS decoder reduces resource utilization by up to 56% compared to the OMS decoder. [ABSTRACT FROM AUTHOR]

This letter describes a practical Slepian-Wolf source coding scheme based on Low Density Parity Check (LDPC) codes. It considers the realistic setup where the parameters of the statistical model between the source and the side information are unknown. A novel Self-Corrected Belief-Propagation (SC-BP) algorithm is proposed in order to make the coding scheme robust to incorrect model parameters by introducing some memory inside the LDPC decoder. A Two Dimensional Density Evolution (2D-DE) analysis is then developed to predict the theoretical performance of the SC-BP decoder. Both the 2D-DE analysis and Monte-Carlo simulations confirm the robustness of the SC-BP decoder. The proposed solution allows for an important complexity reduction and shows a performance very close to existing methods which jointly estimate the model parameters and the source sequence. [ABSTRACT FROM AUTHOR]

Impulsive noise (IN) constitutes a limiting factor in power-line communication systems, especially in those relying on orthogonal frequency division multiplexing (OFDM). If a single time-domain sample is contaminated by an impulse, all subcarriers become contaminated after the spreading of the discrete Fourier transform-based demodulation. In order to alleviate this problem, hybrid automatic repeat-and-request (HARQ) is often invoked. Moreover, the powerful low-density parity-check (LDPC) codes have been increasingly employed in a variety of current and next-generation communication standards. Against this background, in this paper, we explicitly characterize the performance of LDPC-coded HARQ-assisted OFDM systems in the face of IN, where the performance metrics of the outage probability (OP) and the average number of retransmissions, as well as the effective throughput, are analyzed. First of all, we conceive a new algorithm for evaluating the OP in a realistic finite-length LDPC regime, by adapting both the so-called density evolution technique and the waterfall signal-to-noise ratio analysis method. Following this, both the average number of retransmission attempts and the effective throughput are investigated based on our analysis of the OP. The accuracy of the proposed analysis is confirmed by the simulation results, which also effectively quantify the impact of IN on HARQ-assisted OFDM systems in a finite-length LDPC regime.

Polar codes asymptotically achieve the symmetric capacity of arbitrary binary-input discrete memoryless channels under low-complexity sequential decoding algorithms such as successive cancellation decoding. However, in their original formulation, the block length of polar codes is limited to integer powers of the dimension of the underlying polarization kernel used, thus imposing strict constraints on possible application scenarios. While leeway in the choice of kernel or concatenation with other codes mitigates this drawback to a certain extent, puncturing presents a promising approach to specify the target length of a polar code with much greater flexibility. In this paper, we present an efficient implementation of the construction of punctured polar codes based on density evolution, a crucial tool in the construction of both regular, i.e., unpunctured, as well as punctured polar codes. Our implementation of density evolution covers the construction of both regular and punctured polar codes and allows for treating the construction of both code classes in a unified framework. Using our implementation, we achieve substantial reductions in the number of density convolutions necessary for the construction of punctured polar codes and obtain tight upper bounds on the block error rates.

In this paper, the problem of using uncoordinated multiple access (UMA) to serve a massive amount of heterogeneous users is investigated. Leveraging the heterogeneity, we propose a novel UMA protocol, called iterative collision resolution for slotted ALOHA (IRSA) with non-orthogonal multiple access (NOMA), to improve the conventional IRSA. In addition to the inter-slot successive interference cancellation (SIC) technique used in existing IRSA-based schemes, the proposed protocol further employs the intra-slot SIC technique that enables collision resolution for certain configurations of collided packets. A novel multi-dimensional density evolution is then proposed to analyze and to optimize the proposed protocol. Simulation results show that the proposed IRSA with NOMA protocol can efficiently exploit the heterogeneity among users and the multi-dimensional density evolution can accurately predict the throughput performance. Last, an extension of the proposed IRSA with NOMA protocol to the frame-asynchronous setting is investigated, where a boundary effect similar to that in spatially-coupled low-density parity check codes can be observed to bootstrap the decoding process. [ABSTRACT FROM AUTHOR]

We consider the optimal design of the frame-based irregular repetition slotted ALOHA (IRSA) protocol for minimizing the average age of information (AAoI) in grant-free massive machine-type communications (mMTC). To this end, we first characterize the AAoI as a function of the number of user elements (UEs), the frame duration, and the repetition distribution of IRSA. We present this characterization for IRSA schemes with packet recovery at the end of frame and packet generation either at the beginning of the frame or just in time before first transmission in a frame. We also propose and characterize the AAoI of a novel early packet recovery method which further reduces the average age of information. In all cases, the analysis reveals that, as a function of normalized channel traffic (defined as the ratio of number of UEs to frame duration), the AAoI first decreases linearly due to more frequent updates received from the UEs, and increases sharply beyond a critical point due to packet recovery failures caused by collisions. We then consider the problem of minimizing AAoI by optimizing over the normalized channel traffic and repetition distribution for all the proposed sampling and recovery schemes. The optimization problem is challenging since the objective function is semi-analytical and can only be completely characterized using simulations. In an asymptotic regime where the number of UEs as well as the frame size is large, we characterize the AAoI using upper and lower bounds. We also obtain a locally optimal normalized channel traffic and repetition distribution using differential evolution. Based on the insights obtained from the asymptotic analysis, we also propose a pragmatic approach to obtain a normalized channel traffic and repetition distribution for AAoI reduction in the non-asymptotic case. Finally, we empirically show that our AAoI minimizing schemes outperform conventional throughput optimal schemes. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of spatially coupled turbo codes, namely partially information- and partially parity-coupled turbo codes. This class of codes enjoy several advantages such as flexible code rate adjustment by varying the coupling ratio and the encoding and decoding architectures of the underlying component codes can remain unchanged. For this work, we first provide the construction methods for partially coupled turbo codes with coupling memory m and study the corresponding graph models. We then derive the density evolution equations for the corresponding ensembles on the binary erasure channel to precisely compute their iterative decoding thresholds. Rate-compatible designs and their decoding thresholds are also provided, where the coupling and puncturing ratios are jointly optimized to achieve the largest decoding threshold for a given target code rate. Our results show that for a wide range of code rates, the proposed codes attain close-to-capacity performance and the decoding performance improves with increasing the coupling memory. In particular, the proposed partially parity-coupled turbo codes have thresholds within 0.0002 of the BEC capacity for rates ranging from 1/3 to 9/10, yielding an attractive way for constructing rate-compatible capacity-approaching channel codes. [ABSTRACT FROM AUTHOR]

Analytic expressions of decoding thresholds both for regular and irregular low-density parity-check (LDPC) codes over the binary erasure channel (BEC) are given, and low-complexity methods for determining the thresholds are proposed based on the analytic expressions. Specifically, firstly, a fixed-point equation, which represents a constraint relationship between the threshold and erasure probability of transmitted bits, is established. Secondly, by introducing an auxiliary equation, the threshold can be solved as an analytically function of solutions of a polynomial equation. Moreover, this method is extended to the Additive White Gaussian Noise (AWGN) channel. Numerical results show that, our proposed method is more accurate, and the complexity is much lower than that of conventional density evolution (DE). Moreover, our method does not require to compute the inverse of degree distribution function for irregular LDPC codes. [ABSTRACT FROM AUTHOR]

We propose a nonuniform quantized decoder for polar codes. The design metric of the quantizers is to minimize the distortion incurred by quantization. The quantizers are obtained via dynamic programming and the optimality of the quantizer is proved as well. Simulation results show that the error correction performance degradation of the proposed nonuniform quantized decoder is less than 0.1 dB compared to conventional float-point decoders under 5-bit nonuniform quantization, outperforming previous uniform quantized decoders for polar codes significantly. [ABSTRACT FROM AUTHOR]

This paper focuses on an improved Gaussian approximation (GA) based construction of polar codes with successive cancellation (SC) decoding over an additive white Gaussian noise (AWGN) channel. Arıkan proved that polar codes with low-complexity SC decoding can approach the channel capacity of an arbitrary symmetric binary-input discrete memoryless channel, provided that the code length is chosen large enough. Nevertheless, how to construct such codes over an AWGN channel with low computational effort has been an open problem. Compared to density evolution, the GA is known as a low complexity yet powerful technique that traces the evolution of the mean log likelihood ratio (LLR) value by iterating a nonlinear function. Therefore, its high-precision numerical evaluation is critical as the code length increases. In this work, by analyzing the asymptotic behavior of this nonlinear function, we propose an improved GA approach that makes an accurate trace of mean LLR evolution feasible. With this improved GA, through numerical analysis and simulations with code lengths up to $N=2^{18}$ , we explicitly demonstrate that various code-rate polar codes with long codeword and capacity approaching behavior can be easily designed. [ABSTRACT FROM AUTHOR]

In this paper, we address a number of weaknesses of the windowed decoding of spatially coupled low-density parity-check (SC LDPC) codes and propose three modifications that simultaneously improve its performance, complexity, and latency. An effective termination method of the windowed decoding and the reuse of edge messages of previous target symbols provide a good performance-latency tradeoff when compared with the conventional windowed decoder. Also, we propose a scheme that lowers the error floor, in which the amplified edge messages of the previous window are used in the present window. The proposed windowed decoding, consisting of the three schemes, provides a significant performance gain with smaller latency. The validity of the new windowed decoding is verified by the evaluation with codes from different SC LDPC ensembles.

Abstract In this paper, a polar-coded space-time transmit diversity (STTD) scheme is proposed in order to improve the performance of multiple-input multiple-output (MIMO) system. In Rician fading MIMO channels, the corresponding polar-coded STTD system can be equivalent to a single transmission channel for each polar code bit. Density evolutions for the polar-coded STTD systems are proposed based on the analyses of the single transmission channel. The proposed density evolutions provide preferable guidance to construct polar codes for the polar-coded STTD systems. Simulation results show that the BER performance of polar-coded STTD system is significantly improved as the number of antennas increases and the influence of the variable Rician K-factor of MIMO channels gradually vanishes. The proposed 2 × 2 polar-coded STTD system can provide better frame error rate (FER) performance than low-density parity-check (LDPC)-based system under low and mid code rates, and the average advantage is 0.3 dB approximately when the code rate is 0.25 and 0.2 dB when the code rate is 0.5.

We propose a two-layer coding architecture for communication of multiple users over a shared slotted medium enabling joint collision resolution and decoding. Each user first encodes its information bits with an outer code for reliability, and then transmits these coded bits with possible repetitions over transmission time slots of the access channel. The transmission patterns are dictated by the inner collision-resolution code and collisions with other users’ transmissions may occur. We analyze two types of codes for the outer layer: long-blocklength LDPC codes, and short-blocklength algebraic codes. With LDPC codes, a density evolution analysis enables joint optimization of both outer and inner code parameters for maximum throughput. With algebraic codes, we invoke a similar analysis by approximating their average erasure correcting capability while assuming a large number of active transmitters. The proposed low-complexity schemes operate at a significantly smaller gap to capacity than the state of the art. Our schemes apply both to a multiple access scenario where the number of users within a frame is known a priori, and to a random access scenario where that number is known only to the decoder. In the latter case, we optimize an outage probability due to the variability in user activity. [ABSTRACT FROM AUTHOR]

Compute-and-forward (CAF) relaying is an effective way to increase bandwidth efficiency of wireless two-way relay channels. Design of error-correcting codes and their decoding algorithms suitable for CAF relaying schemes remains an important issue to be studied. In this paper, we will analyze an asymptotic behavior of LDPC codes over two-way relay channels based on density evolution (DE). Because of the asymmetric characteristics of the channel, we use the population dynamics DE combined with DE formulas for asymmetric channels to obtain the belief propagation (BP) thresholds. Additionally, we also evaluate the asymptotic performance of spatially coupled LDPC codes for two-way relay channels. The results indicate that the spatially coupled codes yield improvements in the BP threshold compared with corresponding uncoupled codes for two-way relay channels. [ABSTRACT FROM AUTHOR]

This paper is concerned with the dynamics of spatially-coupled low-density parity-check (SC-LDPC) ensembles for transmission on general binary memoryless symmetric (BMS) channels under belief-propagation (BP) decoding. The decoding waves of such ensembles are found to exhibit solitonic behavior, propagating along the Tanner graphs at asymptotically constant velocities. A low-complexity approach termed interpolated density evolution (IDE) is proposed to predict the decoding wave velocities. In this approach, the densities of a decoding wave are approximated by interpolating between some fixed points of an uncoupled DE recursion with one-dimensional functions. Two transfer functions for updating these interpolation functions in the IDE recursion are established and a simple strategy is introduced to deal with the coexistence of multiple transition regions. In addition, a threshold analysis is developed based on two ansatzes, explaining why our approach can achieve a good trade-off between computational cost and accuracy, as illustrated with some numerical examples at the end of this paper. [ABSTRACT FROM AUTHOR]

The practical NAND flash memory suffers from various non-stationary noises that are difficult to be predicted. For example, the data retention noise induced channel offset is unknown during the readback process, and hence severely affects the reliability of data recovery from the memory cell. In this paper, we first propose a novel recurrent neural network (RNN)-based detector to effectively detect the data stored in the multi-level-cell (MLC) flash memory without the prior knowledge of the channel. However, compared with the conventional threshold detector, the proposed RNN detector introduces much longer read latency and more power consumption. To tackle this problem, we further propose an RNN-aided (RNNA) dynamic threshold detector, whose detection thresholds can be derived based on the outputs of the RNN detector. We thus only need to activate the RNN detector periodically when the system is idle. Moreover, to enable soft-decision decoding of error-correction codes, we first show how to obtain more read thresholds based on the hard-decision read thresholds derived from the RNN detector. We then propose integer-based reliability mappings based on the designed read thresholds, which can generate the soft information of the channel. Finally, we propose to apply density evolution (DE) combined with the differential evolution algorithm to optimize the read thresholds for low-density parity-check (LDPC) coded flash memory channels. Computer simulation results demonstrate the effectiveness of our proposed RNNA dynamic read thresholds design, for both the uncoded and LDPC-coded flash memory channels, without any prior knowledge of the channel. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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Bilayer low-density parity-check (LDPC) codes are an effective coding technique for decode-and-forward relaying, where the relay forwards extra parity bits to help the destination to decode the source bits correctly. In the existing bilayer coding scheme, these parity bits are protected by an error correcting code and assumed reliably available at the receiver. We propose an uncoded relaying scheme, where the extra parity bits are forwarded to the destination without any protection. Through density evolution analysis and simulation results, we show that our proposed scheme achieves better performance in terms of bit erasure probability than the existing relaying scheme. In addition, our proposed scheme results in lower complexity at the relay.

Low Density Parity Check (LDPC) codes are currently being deeply analyzed through algorithms that require the capability of addressing their iterative decoding convergence performance. Since it has been observed that the probability distribution function of the decoder’s log-likelihood ratio messages is roughly Gaussian, a multiplicity of moderate entanglement strategies to this analysis has been suggested. The first of them was proposed in Chung et al.’s 2001 paper, where the recurrent sequence, characterizing the passage of messages between variable and check nodes, concerns the function ϕ(x), therein specified, and its inverse. In this paper, we review this old approximation to the function ϕ(x), one variant on it obtained in the same period (proposed in Ha et al.’s 2004 paper), and some new ones, recently published in two 2019 papers by Vatta et al. The objective of this review is to analyze the differences among them and their characteristics in terms of accuracy and computational complexity. In particular, the explicitly invertible, not piecewise defined approximation of the function ϕ(x), published in the second of the two abovementioned 2019 papers, is shown to have less relative error in any x than most of the other approximations. Moreover, its use conducts to an important complexity reduction, and allows better Gaussian approximated thresholds to be obtained.

In this paper, we analyze the waterfall performance of finite-length low-density parity-check (LDPC) codes for asymmetric memoryless channels by considering variations of channel parameters: the observed bit error rate $P_{\text{obs}}$ and mutual information $I_{\text{obs}}$ during the real-time transmission. Moreover, we propose to use the variation of a new channel parameter: the maximal achievable channel coding rate $R_{\text{obs}}$ at finite blocklengths to estimate the waterfall performance. Simulation results demonstrate that our estimations can well predict the waterfall performance of LDPC codes. In particular, the estimation based on $R_{\text{obs}}$ can fit the waterfall performance for various code lengths. For estimations based on $P_{\text{obs}}$ and $I_{\text{obs}}$ , their accuracy increases as the codeword length increases and no curve fitting is required. [ABSTRACT FROM AUTHOR]

As emerging memories such as spin-torque transfer magnetic random access memory (STT-MRAM) suffer from reliability issues caused by process variations and thermal fluctuations, the design of channel quantizer with the minimum number of quantization bits is critical to support effective error correction coding for ensuring high-density and high-speed memory data storage. In this paper, we first propose a quantized channel model for STT-MRAM. Based on the quantized channel model, we derive various information theoretic bounds, including the mutual information, cutoff rate, and the Polyanskiy-Poor-Verdú (PPV) finite-length performance bound. By using these bounds as design criteria, we optimize the quantizer design for the polar-coded STT-MRAM channel. Moreover, we also propose a polar-code-specific quantization design with the successive cancellation decoding algorithm, by using the block error probability bound obtained from density evolution (DE). Simulation results show that all our proposed quantizers generally outperform the prior art greedy merging quantizer. In addition, both the cutoff rate and PPV bound based quantizers outperform the most widely applied mutual information based quantizer for short-length polar codes with 2-bit quantization. Furthermore, the DE quantizer designed specifically for polar codes achieves the best performance among all the proposed quantizers. [ABSTRACT FROM AUTHOR]

Since multi-edge type low-density parity-check (MET-LDPC) codes were first proposed, the design of MET-LDPC codes has been extensively studied for various applications. However, the existing design rules assume that check node degrees are in the so-called concentrated form which enables one to conveniently find pairs of edge and node distributions satisfying the socket count equalities (SCEs). However, it in return makes the code design conducted in a limited search space, which may lead to a sub-optimal design. This paper proposes a novel design rule for MET-LDPC codes together with a scheme to efficiently sort out invalid distributions, i.e., ones not satisfying the SCEs, in the design process. The proposed design rule does not require check node degrees to be in the concentrated form and can find out optimized MET-LDPC codes without any restriction on the search space. Based on the proposed design rule, MET-LDPC codes are designed across a wide range of code rates on binary-erasure channel and binary-input additive-white Gaussian channel. The designed codes are compared with ones reported in the open literature, which confirms that MET-LDPC codes with the proposed design rule have better threshold performances regardless of channel and code rate even with sets of limited code parameters. [ABSTRACT FROM AUTHOR]