A novel hard decision decoding scheme based on genetic algorithm and neural network

A novel hard decision decoding scheme based on a hybrid intelligent algorithm combining genetic algorithm and neural network, named as genetic neural-network decoding (GND), is proposed. GND offsets the reliability loss caused by channel transmission error and hard decision quantization by making full use of the genetic algorithm's optimization capacity and neural network's pattern classification function to optimize the hard decision outputs of received matched filter and restore a more likelihood codeword as the input of hard decision decoder. As can be seen from the theoretical analysis and computer simulation, GND scheme is close to the traditional soft decision decoding in error correction performance, while its complexity, compared with the traditional soft decision decoding, is greatly reduced because its decoding process does not need to use the channel statistical information.     

Protograph bit-interleaved coded modulation: A bandwidth-efficient design paradigm for 6G wireless communications

Bit-interleaved coded modulation (BICM) has attracted considerable attention from the research community in the past three decades, because it can achieve desirable error performance with relatively low implementation complexity for a large number of communication and storage systems. By exploiting the iterative demapping and decoding (ID), the BICM is able to approach capacity limits of coded modulation over various channels. In recent years, protograph low-density parity-check (PLDPC) codes and their spatially-coupled (SC) variants have emerged to be a pragmatic forward-error-correction (FEC) solution for BICM systems due to their tremendous error-correction capability and simple structures, and found widespread applications such as deep-space communication, satellite communication, wireless communication, optical communication, and data storage. This article offers a comprehensive survey on the state-of-the-art development of PLDPC-BICM and its innovative SC variants over a variety of channel models, e.g., additive white Gaussian noise (AWGN) channels, fading channels, Poisson pulse position modulation (PPM) channels, and flash-memory channels. Of particular interest is code construction, constellation shaping, as well as bit-mapper design, where the receiver is formulated as a serially-concatenated decoding framework consisting of a soft-decision demapper and a belief-propagation decoder. Finally, several promising research directions are discussed, which have not been adequately addressed in the current literature.     

Joint Early Stopping Criterions for Protograph LDPC Codes-Based JSCC System in Images Transmission

In this paper, a joint early stopping criterion based on cross entropy (CE), named joint CE criterion, is presented for double-protograph low-density parity-check (DP-LDPC) codes-based joint source-channel coding (JSCC) systems in images transmission to reduce the decoding complexity and decrease the decoding delay. The proposed early stopping criterion adopts the CE from the output likelihood ratios (LLRs) of the joint decoder. Moreover, a special phenomenon named asymmetry oscillation-like convergence (AOLC) in the changing process of CE is uncovered in the source decoder and channel decoder of this system meanwhile, and the proposed joint CE criterion can reduce the impact from the AOLC phenomenon. Comparing to the counterparts, the results show that the joint CE criterion can perform well in the decoding complexity and decoding latency in the low–moderate signal-to-noise ratio (SNR) region and achieve performance improvement in the high SNR region with appropriate parameters, which also demonstrates that this system with joint CE is a low-latency and low-power system.     

基于超结构光纤光栅的正交四相光码分多址编/解码器

正交四相序列编码相比于二相序列具有更大的码字容量和更好的互相关特性,因此更适用于光码分多址(OCDMA)无源光接入网.提出并实现了一种基于超结构光纤光栅的正交四相光码分多址编/解码器.该编/解码器采用A族四相序列作为地址码,在制作的过程中仅需一个均匀相位掩模板即可实现编码功能,并且在性能上与传统工艺制作的编码器相当.为了与不同波长信道相匹配,提出了变信道编码技术,仿真结果表明采用该技术的编码器具有更高频谱效率,因此得到更好的编/解码性能.对一个码长63,长度4.1 cm的正交四相编/解码器进行了信息速率为2.5 Gb/s.码片速率为156 Gchip/s的编/解码实验,取得了较好的编/解码效果.     

Deep neural network-based detection of index modulated MIMO-OFDM

Multiple-input multiple-output orthogonal frequency division multiplexing with index modulation (MIMO-OFDM-IM) has been introduced as a new transmission method for 5G and beyond communications. On the other hand, deep neural networks (DNNs) have started to be effective in many fields, including wireless communication, due to their advantages such as low complexity, high performance, low processing times, etc. Since the optimum decoding for MIMO-OFDM-IM grows exponentially with higher modulation orders and the number of transmit and receive antennas, DNN-based decoding will be a potential choice for the next generation receiver architecture. In this work, a novel fully connected DNN based MIMO-OFDM-IM to jointly detect the transmitted symbols from each antenna is proposed and its performance is analyzed. As seen from the simulation results, the proposed DNN-based detector shows a close bit error rate performance to optimum detection with lower computational complexity.     

Improving Log-Likelihood Ratio Estimation with Bi-Gaussian Approximation under Multiuser Interference Scenarios

Accurate estimation of channel log-likelihood ratio (LLR) is crucial to the decoding of modern channel codes like turbo, low-density parity-check (LDPC), and polar codes. Under an additive white Gaussian noise (AWGN) channel, the calculation of LLR is relatively straightforward since the closed-form expression for the channel likelihood function can be perfectly known to the receiver. However, it would be much more complicated for heterogeneous networks where the global noise (i.e., noise plus interference) may be dominated by non-Gaussian interference with an unknown distribution. Although the LLR can still be calculated by approximating the distribution of global noise as Gaussian, it will cause performance loss due to the non-Gaussian nature of global noise. To address this problem, we propose to use bi-Gaussian (BG) distribution to approximate the unknown distribution of global noise, for which the two parameters of BG distribution can easily be estimated from the second and fourth moments of the overall received signals without any knowledge of interfering channel state information (CSI) or signaling format information. Simulation results indicate that the proposed BG approximation can effectively improve the word error rate (WER) performance. The gain of BG approximation over Gaussian approximation depends heavily on the interference structure. For the scenario of a single BSPK interferer with a 5 dB interference-to-noise ratio (INR), we observed a gain of about 0.6 dB. The improved LLR estimation can also accelerate the convergence of iterative decoding, thus involving a lower overall decoding complexity. In general, the overall decoding complexity can be reduced by 25 to 50%.     

量子稀疏图码的反馈式迭代译码

量子稀疏图码的译码可以由基于错误图样的和积译码算法来实现.本文在此基础上构建了一个新的反馈式迭代译码算法.其反馈策略不仅仅重新利用了错误图样,而且还利用了稳定子上相应元素的值和信道的错误模型.由此,本方法一方面可以克服传统的量子和积译码算法中遇到的所谓对称简并错误,另一方面还能反馈更多的有用信息到译码器中,帮助其产生有效的译码结果,大大提高译码器的译码能力.另外,本算法并没有增加量子测量的复杂度,而是对测量中所能获得的信息的更充分利用.     

A resource-saving decoding scheme of the orthogonally concatenated codes for optical transport networks in FPGA

A decoding scheme of the orthogonally concatenated codes with low resource utilizations is proposed. In the optical transport networks (OTN), forward error-correction (FEC) techniques are used to reduce the errors which occur in transmissions. Two-orthogonal-concatenated (TOC) codes are widely used in FEC techniques for their powerful error-correction capabilities based on the iterative decoding procedure. However, the framing structure is complex so the decoding procedure is more difficult than the decoding of in–out concatenated codes. And the powerful error-correction capability relies on the multi-iterative decoding processing, thus how to effectively utilize the hardware resources is a very important problem. Especially when the decoding procedure is implemented in the field programmable gate array (FPGA) devices, effective optimizations are required for the limited resources. In this paper we present an iterative decoding scheme in FPGA with low resource utilizations. As an example, an actual engineering application under the G.975.1 recommendation is given to show the efficiency of the proposed design.     

Performance analysis of LDPC codes on OOK terahertz wireless channels

Atmospheric absorption, scattering, and scintillation are the major causes to deteriorate the transmission quality of terahertz(THz) wireless communications. An error control coding scheme based on low density parity check(LDPC) codes with soft decision decoding algorithm is proposed to improve the bit-error-rate(BER) performance of an on-off keying(OOK) modulated THz signal through atmospheric channel. The THz wave propagation characteristics and channel model in atmosphere is set up. Numerical simulations validate the great performance of LDPC codes against the atmospheric fading and demonstrate the huge potential in future ultra-high speed beyond Gbps THz communications.     

Trade-offs between Error Exponents and Excess-Rate Exponents of Typical Slepian–Wolf Codes

Typical random codes (TRCs) in a communication scenario of source coding with side information in the decoder is the main subject of this work. We study the semi-deterministic code ensemble, which is a certain variant of the ordinary random binning code ensemble. In this code ensemble, the relatively small type classes of the source are deterministically partitioned into the available bins in a one-to-one manner. As a consequence, the error probability decreases dramatically. The random binning error exponent and the error exponent of the TRCs are derived and proved to be equal to one another in a few important special cases. We show that the performance under optimal decoding can be attained also by certain universal decoders, e.g., the stochastic likelihood decoder with an empirical entropy metric. Moreover, we discuss the trade-offs between the error exponent and the excess-rate exponent for the typical random semi-deterministic code and characterize its optimal rate function. We show that for any pair of correlated information sources, both error and excess-rate probabilities exponential vanish when the blocklength tends to infinity.     

基于超结构光纤光栅的全光编解码性能分析

分析了光码分多址(OCDMA)系统中超结构光纤光栅(SSFBG)编解码器的相关特性, 考虑了输入脉冲宽度、SSFBG编解码光栅之间的波长偏移以及光栅的折射率调制振幅对全光编解码性能的影响。结果表明, 随着输入脉冲宽度和编解码光栅之间的波长偏移量的增加, 自相关峰值旁瓣比和自互相关峰值比下降, 即编解码性能出现下降; 编解码器的插入损耗和相关性能间存在矛盾, 需要折中考虑SSFBG折射率调制振幅的选取。建立了基于SSFBG编解码器的时域相位编码OCDMA系统的数学模型, 考虑了差拍噪声、多址干扰、接收机噪声以及接收机的带宽限制对系统性能的影响, 采用全光阈值技术和turbo编码来提高相干扩时OCDMA的系统性能。     

Soft Interference Cancellation for Random Coding in Massive Gaussian Multiple-Access

In 2017, Polyanskiy showed that the trade-off between power and bandwidth efficiency for massive Gaussian random access is governed by two fundamentally different regimes: low power and high power. For both regimes, tight performance bounds were found by Zadik et al., in 2019. This work utilizes recent results on the exact block error probability of Gaussian random codes in additive white Gaussian noise to propose practical methods based on iterative soft decoding to closely approach these bounds. In the low power regime, this work finds that orthogonal random codes can be applied directly. In the high power regime, a more sophisticated effort is needed. This work shows that power-profile optimization by means of linear programming, as pioneered by Caire et al. in 2001, is a promising strategy to apply. The proposed combination of orthogonal random coding and iterative soft decoding even outperforms the existence bounds of Zadik et al. in the low power regime and is very close to the non-existence bounds for message lengths around 100 and above. Finally, the approach of power optimization by linear programming proposed for the high power regime is found to benefit from power imbalances due to fading which makes it even more attractive for typical mobile radio channels.     

FPGA-Implemented Fractal Decoder with Forward Error Correction in Short-Reach Optical Interconnects

Forward error correction (FEC) codes combined with high-order modulator formats, i.e., coded modulation (CM), are essential in optical communication networks to achieve highly efficient and reliable communication. The task of providing additional error control in the design of CM systems with high-performance requirements remains urgent. As an additional control of CM systems, we propose to use indivisible error detection codes based on a positional number system. In this work, we evaluated the indivisible code using the average probability method (APM) for the binary symmetric channel (BSC), which has the simplicity, versatility and reliability of the estimate, which is close to reality. The APM allows for evaluation and compares indivisible codes according to parameters of correct transmission, and detectable and undetectable errors. Indivisible codes allow for the end-to-end (E2E) control of the transmission and processing of information in digital systems and design devices with a regular structure and high speed. This study researched a fractal decoder device for additional error control, implemented in field-programmable gate array (FPGA) software with FEC for short-reach optical interconnects with multilevel pulse amplitude (PAM-M) modulated with Gray code mapping. Indivisible codes with natural redundancy require far fewer hardware costs to develop and implement encoding and decoding devices with a sufficiently high error detection efficiency. We achieved a reduction in hardware costs for a fractal decoder by using the fractal property of the indivisible code from 10% to 30% for different n while receiving the reciprocal of the golden ratio.     

List Decoding of Arıkan’s PAC Codes

Polar coding gives rise to the first explicit family of codes that provably achieve capacity with efficient encoding and decoding for a wide range of channels. However, its performance at short blocklengths under standard successive cancellation decoding is far from optimal. A well-known way to improve the performance of polar codes at short blocklengths is CRC precoding followed by successive-cancellation list decoding. This approach, along with various refinements thereof, has largely remained the state of the art in polar coding since it was introduced in 2011. Recently, Arıkan presented a new polar coding scheme, which he called polarization-adjusted convolutional (PAC) codes. At short blocklengths, such codes offer a dramatic improvement in performance as compared to CRC-aided list decoding of conventional polar codes. PAC codes are based primarily upon the following main ideas: replacing CRC codes with convolutional precoding (under appropriate rate profiling) and replacing list decoding by sequential decoding. One of our primary goals in this paper is to answer the following question: is sequential decoding essential for the superior performance of PAC codes? We show that similar performance can be achieved using list decoding when the list size L is moderately large (say, L⩾128). List decoding has distinct advantages over sequential decoding in certain scenarios, such as low-SNR regimes or situations where the worst-case complexity/latency is the primary constraint. Another objective is to provide some insights into the remarkable performance of PAC codes. We first observe that both sequential decoding and list decoding of PAC codes closely match ML decoding thereof. We then estimate the number of low weight codewords in PAC codes, and use these estimates to approximate the union bound on their performance. These results indicate that PAC codes are superior to both polar codes and Reed–Muller codes. We also consider random time-varying convolutional precoding for PAC codes, and observe that this scheme achieves the same superior performance with constraint length as low as ν=2.     

Model and comparative analysis of reduced-complexity receiver designs for the LTE-advanced SC-FDMA uplink

Due to its favorable peak-to-average power ratio (PAPR), a single-carrier frequency-division multiple access (SC-FDMA) scheme has been chosen for the 3GPP Long Term Evolution Advanced (LTE-A) uplink, as opposed to the orthogonal frequency-division multiple access (OFDMA) scheme used in the downlink. SC-FDMA, however, is prone to suffer from the effects of inter-symbol interference. When combined with multiple-input multiple-output (MIMO) transmission, the complexity of optimal detection for SC-FDMA grows exponentially with the product of the number of transmitting antennas and the channel length. A means to reduce the complexity is to equalize the channel in the frequency domain first, similar to OFDMA, followed by detection in the time domain, using well-developed standard receivers for flat fading MIMO channels. Apparently, these reduced-complexity two-stage receivers suffer from a rate loss as a consequence of their simplifying design assumptions. In this paper, we provide an extensive model of SC-FDMA transmission with frequency domain equalization (FDE). Based on this model, we derive the achievable rates of four reduced-complexity two-stage receivers within the mismatched receiver framework in terms of generalized mutual information (GMI). The rate expressions allow us to assess the rate loss as compared to the optimal receiver for varying channel parameters such as channel length and spatial correlation. It is shown, for instance, that a distributed subcarrier mapping which is beneficial from a frequency diversity point of view substantially deteriorates the achievable rates. It is also explained how this loss can be compensated for by combining time-domain detection with frequency-domain interference cancelation.     

Near optimal performance joint semi-blind channel estimation and data detection techniques for Alamouti coded single-carrier (SC) MIMO communication systems

In this paper, two novel joint semi-blind channel estimation and data detection techniques are proposed and investigated for Alamouti coded single-carrier (SC) multiple-input multiple-output (MIMO) communication system using Rayleigh flat fading channel model. In the first novel semi-blind technique, blind channel estimation can be performed by using singular value decomposition (SVD) of received output autocorrelation matrix and training based channel estimation for orthogonal training symbols can be performed by using orthogonal pilot maximum likelihood (OPML) algorithm. Further using, that semi-blind channel estimate and received output, data detection is performed by using Maximum likelihood (ML) detection. Finally we derived new training symbols from error covariance matrix of estimated data and known orthogonal training symbols, which further applied to OPML algorithm for final channel estimate. In the second novel semi-blind technique, blind channel estimation can be performed by using matrix triangularization based on householder QR decomposition (H-QRD) of received output autocorrelation matrix instead of SVD decomposition. Other steps are same as the first novel technique to calculate data detection and final channel estimation. Simulation results are presented under 2-PSK, 4-PSK, 8-PSK and 16-QAM data modulation schemes using 2 transmitters and different combinations of receiver antennas to investigate the performances of novel techniques compare to conventional whitening rotation (WR) and rotation optimization maximum likelihood (ROML) based semi-blind channel estimation techniques. Result demonstrates that novel techniques outperform others by achieving near optimal performance.     

A Generalized Spatial Modulation System Using Massive MIMO Space Time Coding Antenna Grouping

Massive multiple input multiple output (MIMO), also known as a very large-scale MIMO, is an emerging technology in wireless communications that increases capacity compared to MIMO systems. The massive MIMO communication technique is currently forming a major part of ongoing research. The main issue for massive MIMO improvements depends on the number of transmitting antennas to increase the data rate and minimize bit error rate (BER). To enhance the data rate and BER, new coding and modulation techniques are required. In this paper, a generalized spatial modulation (GSM) with antenna grouping space time coding technique (STC) is proposed. The proposed GSM-STC technique is based on space time coding of two successive GSM-modulated data symbols on two subgroups of antennas to improve data rate and to minimize BER. Moreover, the proposed GSM-STC system can offer spatial diversity gains and can also increase the reliability of the wireless channel by providing replicas of the received signal. The simulation results show that GSM-STC achieves better performance compared to conventional GSM techniques in terms of data rate and BER, leading to good potential for massive MIMO by using subgroups of antennas.     

DSP based receiver implementation for OFDM acoustic modems

Significant progress has been made recently on the use of multicarrier modulation in the form of orthogonal frequency division multiplexing (OFDM) for high data rate underwater acoustic communications. In this paper, we present implementation results of OFDM acoustic modems under different settings with either one or two parallel data streams transmitted, whose data rate is 3.2 KB/s or 6.4 KB/s, respectively, with QPSK modulation, rate-1/2 channel coding, and signal bandwidth of 6 kHz. To achieve real time operation, the processing time for each OFDM block shall be (much) less than the block duration of 210 ms. We first implement the receiver algorithms on a floating point TMS320C6713 DSP development board, running at 225 MHz. With convolutional coding, the per-block processing time is about 38 ms and 77 ms for single-input single-output (SISO) and multi-input multi-output (MIMO) settings, respectively, where there are two transmitters and two receivers in the latter case. With nonbinary low-density parity-check (LDPC) coding, which gains about 2 dB in error performance relative to convolutional coding, the per-block processing time increases to 50 ms and 101 ms for SISO and MIMO settings, respectively. We have also implemented the receiver algorithms using a fixed-point TMS320C6416 DSP development board, where the DSP core runs at 1 GHz. The per-block processing time reduces by two thirds with negligible performance degradation.     

Low-loss belief propagation decoder with Tanner graph in quantum error-correction codes

Quantum error-correction codes are immeasurable resources for quantum computing and quantum communication.However,the existing decoders are generally incapable of checking node duplication of belief propagation(BP)on quantum low-density parity check(QLDPC)codes.Based on the probability theory in the machine learning,mathematical statistics and topological structure,a GF(4)(the Galois field is abbreviated as GF)augmented model BP decoder with Tanner graph is designed.The problem of repeated check nodes can be solved by this decoder.In simulation,when the random perturbation strength p=0.0115-0.0116 and number of attempts N=60-70,the highest decoding efficiency of the augmented model BP decoder is obtained,and the low-loss frame error rate(FER)decreases to 7.1975×10^-5.Hence,we design a novel augmented model decoder to compare the relationship between GF(2)and GF(4)for quantum code[[450,200]]on the depolarization channel.It can be verified that the proposed decoder provides the widely application range,and the decoding performance is better in QLDPC codes.     

WDM compatible and electrically tunable SPE-OCDMA system based on the temporal self-imaging effect

A coding/decoding setup for a spectral phase encoding optical code-division multiple access (SPE-OCDMA) system has been developed. The proposal is based on the temporal self-imaging effect and the use of an easily tunable electro-optic phase modulator to achieve line-by-line coding of the transmitted signal, thus assuring compatibility with WDM techniques. Modulation of the code is performed at the same rate as the data, avoiding the use of high-bandwidth electro-optic modulators. As proof of concept of the technique, experimental results are presented for a back-to-back coder/decoder setup transmitting a 10 GHz unmodulated optical pulse train within an 80 GHz optical window and using 8-chip Hadamard codes.