Forward Error Correction Codes Research Articles

Performance Analysis of BER and SNR Performance in High-QAM Modulations Using Advancements in MIMO Systems

Wireless communications is one of the most active areas of technology development of our time. This development is being driven primarily by the transformation of what has been largely a medium for supporting voice telephony into a medium for supporting other services, such as the transmission of video, images, text, and data. Today, the widely deployed network type is based on a centralized approach that requires a network point of access, commonly called the Access Point (AP), to serves as a gateway between the mobile device and the Internet. The obtained results demonstrate that spatial diversity along with the power of STBC significantly improves the error performance in frequency selective wireless fading channels. The BER level is depend on the modulation type, SNR value and channel behavior. Modulation schemes that we have used in this paper are 4-QAM, 8-QAM, 16-QAM and 64-QAM which further improved using forward error correction codes (FEC). A comparison is made between the diversity gains of MIMO systems in terms of BER for high QAM modulation scheme. This work presents, a simulation toll MATLAB R2023a used for model implemented using Nakagami channel to study the performance analysis of Bit Error rate (BER) V/S Signal to Noise ratio (SNR). Keywords: AWGN, BER, Fading Channel, MIMO System, Nakagami, OFDM, QAM Modulation, SNR, STBC etc.

Low-complexity and low-latency equalization technique - probabilistic noise cancellation.

Both inside data centers (DCs) and in short optical links between data centers (DC campuses), intensity-modulation and direct-detection (IMDD) systems using four-level pulse amplitude modulation (PAM4) will dominate this decade due to low transceiver price and power consumption. The next DC transceiver generation based on 100 Gbaud PAM4 will require advanced digital signal processing (DSP) algorithms and more powerful forward error correction (FEC) codes. Because of bandwidth limitations, the conventional DC DSP based on a few-tap linear feed-forward equalizer (FFE) is likely to be upgraded to more complex but still low-complexity Volterra equalizers followed by a noise whitening filter and either a maximum likelihood sequence estimation (MLSE) or a maximum a posteriori probability (MAP) algorithm. However, stringent power consumption and latency requirements may limit the use of complex algorithms such as decision feedback equalizer (DFE) or MLSE/MAP in DC networks (DCN). In this paper, we introduce a low-complexity, low-latency algorithm based on a feedforward structure, yielding a performance between DFE and MLSE. We call the novel equalization algorithm probabilistic noise cancellation (PNC), since it weights noise patterns based on their probabilities in the presence of bandwidth limitations. The probabilistic weighting is efficiently exploited in correcting correlated errors caused by noise coloring in the FFE.

XPM estimation and compensation in the WDM system based on a low-complexity inner FEC.

In this work, we focus on compensation of inter-channel nonlinearity in optical wavelength division multiplexed (WDM) systems. We consider pre-coding with a high-rate forward error correction (FEC) code and a low-complexity and low-latency decoding and equalization scheme at the receiver. The 2 × 2 multiple-input multiple-output (MIMO) recursive least square (RLS) equalizer is applied to reduce the inter-symbol interference (ISI) caused by the inter-channel nonlinearity, while the decoder improves the quality of the data feedback. Decisions based on feedback reliability have been implemented to prevent error propagation. We demonstrate that our system can readily utilize the inner FEC part of a mainstream concatenated optical FEC designs such as the 400ZR standard FEC. We evaluate the proposed algorithm for the dual-polarization 16QAM and 256QAM optical links. Based on our simulation results, the Q-factor has been increased by 0.36 and 0.67 dB for the 16QAM and 256QAM, respectively. The optimum launch power has been increased by 0.4 dB for both cases.

Secure key distribution exploiting error rate criticality for radio frequency links.

We propose a method by which two radio frequency (RF) communication terminals exchange encryption keys or other data securely. This method draws on the approach developed for quantum key distribution (QKD) for detecting eavesdroppers but our method does not use any quantum properties at all. Instead, by exploiting the effects an eavesdropper has on channel stability, we explore a line-of-sight link radio in which data transfer rates are so high as to approach the Shannon limit. With very steep rises in bit error rate accompanying a small degradation of signal-to-noise limits for certain forward error correction codes, it becomes possible to infer the existence of an eavesdropper before they are able to obtain a complete key. We describe our method and analyse one possible implementation using low density parity check codes with quadrature phase shift keying modulation. The proposed technique is in principle far easier to implement than quantum-based approaches for RF and optical wireless links since the required hardware is readily available and the basic principles are well known and well understood. Finally, we show our method to have a higher key rate and spectral efficiency than those of QKD.

200 Gb/s Optical-Amplifier-Free IM/DD Transmissions Using a Directly Modulated O-Band DFB+R Laser Targeting LR Applications

We experimentally demonstrate an O-band single-lane 200 Gb/s intensity modulation direct detection (IM/DD) transmission system using a low-chirp, broadband, and high-power directly modulated laser (DML). The employed laser is an isolator-free packaged module with over 65-GHz modulation bandwidth enabled by a distributed feedback plus passive waveguide reflection (DFB+R) design. We transmit high baud rate signals over 20-km standard single-mode fiber (SSMF) without using any optical amplifiers and demodulate them with reasonably low-complexity digital equalizers. We generate and detect up to 170 Gbaud non-return-to-zero on-off-keying (NRZ-OOK), 112 Gbaud 4-level pulse amplitude modulation (PAM4), and 100 Gbaud PAM6 in the optical back-to-back configuration. After transmission over the 20-km optical-amplifier-free SSMF link, up to 150 Gbaud NRZ-OOK, 106 Gbaud PAM4, and 80 Gbaud PAM6 signals are successfully received and demodulated, achieving bit error rate (BER) performance below the 6.25%-overhead hard-decision (HD) forward-error-correction code (FEC) limit. The demonstrated results show the possibility of meeting the strict requirements towards the development of 200Gb/s/lane IM/DD technologies, targeting 800Gb/s and 1.6Tb/s LR applications.

Efficient LLR Approximation for Coded Constant Envelope OFDM

Constant envelope orthogonal frequency division multiplexing (CE-OFDM) is a promising technique to address the problem of high peak-to-average power ratio (PAPR) by embedding information into the phases of carriers since it was proposed. Meanwhile, in order to further enhance the bit error rate (BER) performance when using forward error correction (FEC) coding, the soft decision should be employed in CE-OFDM systems. However, due to the nonlinear noise in the phase of CE-OFDM, inaccurate log-likelihood ratios (LLRs) cause degradation of the decoding performance. To alleviate this problem, the systematic cause analysis of the phase noise is conducted followed by an efficient phase-noise oriented (PNO) algorithm for the phase demodulator in the CE-OFDM system. We further propose another stationary region Max-log-MAP (SR-MLM) algorithm with the phase unwrapper towards low implementation costs. Simulation results demonstrate that the proposed LLR approximation algorithms are capable of improving the BER performance of coded CE-OFDM compared to its conventional counterpart.

Optimizing Resource Allocation With High-Reliability Constraint for Multicasting Automotive Messages in 5G NR C-V2X Networks

Cellular vehicle-to-everything (C-V2X) has been continuously evolving since Release 14 of the 3 rd Generation Partnership Project (3GPP) for future autonomous vehicles. Apart from automotive safety, 5 G NR further bring new capabilities to C-V2X for autonomous driving, such as real-time local update, and coordinated driving. These capabilities rely on the provision of low latency and high reliability from 5 G NR. Among them, a basic demand is broadcasting or multicasting environment update messages, such as cooperative perception data, with high reliability and low latency from a Road Side Unit (RSU) or a base station (BS). In other words, broadcasting multiple types of automotive messages with high reliability and low latency is one of the key issues in 5 G NR C-V2X. In this work, we consider how to select Modulation and Coding Scheme (MCS), RSU/BS, Forward Error Correction (FEC) code rate, to maximize the system utility, which is a function of message delivery reliability. We formulate the optimization problem as a nonlinear integer programming problem. Since the optimization problem is NP-hard, we propose an approximation algorithm, referred to as the Hyperbolic Successive Convex Approximation (HSCA) algorithm, which uses the successive convex approximation to find the optimal solution. In our simulations, we compare the performance of HSCA with those of three algorithms respectively, including the baseline algorithm, the heuristic algorithm, and the optimal solution. Our simulation results show that HSCA outperforms the baseline and the heuristic algorithms and is very competitive to the optimal solution.

A Review of Modern and Recent Studies on the Low-Density Parity-Check Technology Approach

Data theory coding is an excellent and well-known branch of study that has produced various crucial solutions to the insoluble challenges of safe data transfers. Last improvements in detecting error techniques have resulted in a significant increase in the use of low-density parity-check (LDPC) code to address critical concerns connected to secure data transfer. Until now, decent efforts have been performed on LDPC codes that target low complexity, high performance, and low bit error rate goals. The final aim of this review is to provide a recent literature understanding of modern improvements previously mentioned and in LDPC encoding and decoding (applicative and theoretical) techniques. A comparative scan of many remarkable LDPC decoding algorithms, 5G standard requirements, popular power management methods, and low-energy LDPC design studies is also shown. Lastly, conclusions are presented by outlining key study results, current concerns, and general thoughts on new research directions possibilities. Index Terms— low-density parity-check encoder/decoder (LDPC), error correction codes (ECC), forward error correction codes (FEC), parity check matrix(PCM).

Hardware Efficient Successive-Cancellation Polar Decoders Using Approximate Computing

Benefiting for its capacity-achieving property, the polar codes have attracted wide attention in various forward error correction (FEC) codes. Although Successive-Cancellation (SC) decoders have low hardware complexity, their limited thoughput leads to low hardware efficiency. In this paper, two novel processing elements (PE) units for SC decoders are proposed by the reconstruction of key functions. Approximate comparator and adder-subtractor are developed in the proposed PEs to further enhance the hardware efficiency of the SC decoders with neglectable bit error rate (BER) performance degradation. The designs are implemented and evaluated on 28nm CMOS technology. Simulation results indicate that the area efficiency of two designs are 17.758r <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {Gb/s/mm^{2}}$ </tex-math></inline-formula> and 14.416r <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathrm {Gb/s/mm^{2}}$ </tex-math></inline-formula> with 1024-bit code length and the code rate r, which are 26.7% and 9.7% better than the state-of-the-art SC implementations. Moreover, the low complexity Fast Simplified SC (Fast-SSC) decoder implemented with proposed approximate PEs has 60.3% area efficiency improvement than the prior Fast-SSC decoders with equivalent BER performance.

Novel Real-Time Decision-Based Carrier Tracking for Software-Defined Radios Using M-ARY QAM Modulation

In this paper, a scalable and real-time decision-based carrier tracking for software defined radio (SDR) for M-ary QAM modulation has been proposed and tested in real-time using the universal software radio peripheral (USRP)-2922. The proposed system provides real-time decision-based carrier tracking for improved efficiency and performance. The real-time transfer of data has been done using the USRP-2922 hardware using the M-ary QAM modulation scheme for data transmission. The novelty of the proposed system is that one can transfer random data (binary bits), text or an image which can be encoded using the desired forward error correction codes (FEC) namely the convolution coding/Viterbi soft decision decoding and the turbo coding/decoding. The proposed novel SDR transceiver system with real-time decision-based carrier tracking shows an improved performance for different parameters such as the bit error rate (BER) and signal to noise ratio (Eb/No).

Real-Time FPGA Investigation of Potential FEC Schemes for 800G-ZR/ZR+ Forward Error Correction

Forward error correction (FEC) performance down to 1e-15 bit error rate (BER) of a open FEC code (OFEC), which was recently proposed for the 800G inter-data center interconnect (DCI) standard, is verified with a 100-piece-FPGA implementation at a record 400-Gbps throughput. Besides the OFEC, we also investigate the cons and pros of the concatenated staircase and Hamming code (CFEC) and multilevel codes (MLC) of a concatenated Low-Density Parity-Check (LDPC) and Turbo Product Code (TPC), which are the candidate schemes for the 800G-ZR FEC. The OFEC performance as a function of decoding iterations of Soft-in Soft-out (SISO) and Hard-in Hard-out (HIHO) is investigated, and FPGA emulations reveal the existence of an error flare of the OFEC with two SISO iterations and an severe error floor with one HIHO iteration even with four SISO iterations. Further investigations on different combinations of SISO and HIHO iterations, revealed that three SISO and two HIHO iterations are the optimal choice. Based on this iteration configuration, we studied the methods that decreasing the test patterns (TP) of SISO decoder and the soft bits to reduce the implementation complexity. Then we proposed the simplified OFEC scheme for 800G-ZR application, providing 1.81e-2 pre-FEC BER threshold with half power dissipation of standard OFEC, achieving a trade-off between the error correction performance and power dissipation. Finally, we investigated the performance of performance enhanced OFEC with 24.3% overhead and 2.5e-2 pre-FEC threshold, and finally, FEC candidates for the 800G-ZR+ applications are studied, indicating that the OFEC and channel polarized multilevel coding (CP MLC) are the most promising schemes.

Experimental Evaluation of JANUS Fast Modes in Very High Acoustic Frequency Bands

This article presents extensive field tests of a fast-mode operation of the JANUS acoustic communication standard where the signals occupy high-frequency bands of 38 kHz spanning from 96 to 134 kHz instead of the nominal frequency band of 4.1 kHz spanning from 9.44 to 13.6 kHz specified in the standard. The fixed 32-chip preamble and the 144-chip baseline JANUS packet utilize the frequency-hopped binary frequency shift keying with 13 frequency pairs as defined in the standard while the cargo packets use the single-carrier <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary phase shift keying modulation with a center frequency of 115 kHz and a symbol rate of 23 ksps or up to 34.5 kb/s information data rate with high-order phase shift keying (PSK) and rate-1/2 forward error correction codes. The original JANUS receiver algorithm is modified to improve the frame/symbol synchronization for the fast mode and increase the decoding success rate of the baseline JANUS packet in difficult multipath channels. More than 10 experiments were conducted using a field-programmable-gate-array-based hardware platform consisting of a single transmit projector and a single receive hydrophone. The experiment results show that the JANUS fast mode worked well with both the original JANUS receiver algorithm and the modified receiver algorithm, yielding zero bit error in most of the baseline JANUS packets. The modified receiver algorithm is able to reduce 30% of error packets to zero error in the experiment experiencing difficult multipath channels where the original JANUS receiver algorithm suffers from large bit error rates (BER). Meanwhile, the cargo packets utilize the linear minimum mean-square error turbo equalizer and achieve a BER around 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> .

Low-complexity soft-output signal detector based on AI-SSOR preconditioned conjugate gradient method over massive MIMO correlated channel

Massive multiple-input multiple-output (MIMO) techniques with a large number of antenna elements at base station (BS) have been proved as an alternative to provide potential opportunity to increase the spectrum and energy efficiency. However, in the system, there generally exists a spatial correlation effect due to insufficient antenna elements spacing and/or the lack of rich scattering at BS. The minimum mean square error (MMSE) method performs signal detection at the expense of large-scale matrix inversion operation. Thus, the conjugate gradient (CG) method has received a lot of attentions to realize the MMSE detection efficiently. Unfortunately, this efficiency can be compromised due to the ill-conditioned equalization matrix of MMSE method over the correlated channel environments. Moreover, the hard output signal detection exhibits a sharply degradation in performance for higher-order quadrature amplitude modulation (QAM). Therefore, the modern communication systems use the soft-output information, i.e., log-likelihood ratio (LLR) along with the forward error-correcting code (FEC) to achieve satisfactory performance. The LLR computation along with a higher-order QAM remains challenging due to the exhaustive search of symbol in the modulation constellation. In this paper, a low-complexity soft-output signal detector based on approximate inverse symmetric successive over-relaxation preconditioned conjugate gradient (AI-SSOR-CG-SOD) method is proposed to realize MMSE method detection for uplink multiuser massive MIMO correlated channel. In the proposed method, a new preconditioner, an AI-SSOR, which is based on the Neumann series approximation of the inverse of the conventional SSOR preconditioner is firstly developed to handle ill-conditioned matrix, and then incorporated with CG method to improve the convergence rate and performance. According to the characteristic of the Gray-coding that adjacent symbols in the constellation set have only one different bit, the constellation set is divided multiple times based on the bits of the inphase and the quadrature components of the symbol, which reduces the complexity of the LLR computation of the transmitted bits by avoiding the exhaustive search process. Simulation results show that the AI-SSOR preconditioner is robust against spatial correlation effect, and the proposed detector converges at 3 iterations. Simulation results also show that the proposed detector achieves a better trade-off between the complexity and the performance compared to other existing detectors.

Low power, less occupying area, and improved speed of a 4-bit router/rerouter circuit for low-density parity-check (LDPC) decoders.

Background: Low-density parity-check (LDPC) codes are more error-resistant than other forward error-correcting codes. Existing circuits give high power dissipation, less speed, and more occupying area. This work aimed to propose a better design and performance circuit, even in the presence of noise in the channel. Methods: In this research, the design of the multiplexer and demultiplexer were achieved using pass transistor logic. The target parameters were low power dissipation, improved throughput, and more negligible delay with a minimum area. One of the essential connecting circuits in a decoShder architecture is a multiplexer (MUX) and a demultiplexer (DEMUX) circuit. The design of the MUX and DEMUX contributes significantly to the performance of the decoder. The aim of this paper was the design of a 4 × 1 MUX to route the data bits received from the bit update blocks to the parallel adder circuits and a 1 × 4 DEMUX to receive the input bits from the parallel adder and distribute the output to the bit update blocks in a layered architecture LDPC decoder. The design uses pass transistor logic and achieves the reduction of the number of transistors used. The proposed circuit was designed using the Mentor Graphics CAD tool for 180 nm technology. Results: The parameters of power dissipation, area, and delay were considered crucial parameters for a low power decoder. The circuits were simulated using computer-aided design (CAD) tools, and the results depicted a significantly low power dissipation of 7.06 nW and 5.16 nW for the multiplexer and demultiplexer, respectively. The delay was found to be 100.5 ns (MUX) and 80 ns (DEMUX). Conclusion: This decoder's potential use may be in low-power communication circuits such as handheld devices and Internet of Things (IoT) circuits.

Coherent Optical Transceivers Scaling and Integration Challenges

The advancement of digital coherent technologies has dramatically increased the system capacity per single-core single-mode fiber to the point that we can now approach the Shannon limit by utilizing high-order modulation formats and high-coding gain forward error correction (FEC) codes. Because the required energy per bit increases exponentially the closer we get to the Shannon limit, extending the available optical bandwidth by using ultrawideband wavelength-division multiplexing (WDM) and/or spatial-division multiplexing (SDM) is indispensable for increasing the system capacity with high energy efficiency. However, simple extensions of wavelength resources and spatial parallelization dramatically increase the number of transceivers (TxRxs) in proportion to the wavelength/spatial multiplicity. The key to achieving cost- and energy-efficient systems is to reduce the system complexity by using high-density integration and broadband optelectronics. In this article, we overview and discuss the recent advances of coherent optical transceivers integrated with an optical front end and digital signal processing (DSP)/application-specific integrated circuit (ASIC). We then present the transponder architectures and the challenges involved in applying them for massive parallelized transmission systems.

Design and Experimental Investigation of Decode-and-Forward and Amplify-and-Forward Relaying FSO-CDMA

The scheme of combining relay and optical code division multiple access (OCDMA) is one of the effective methods to improve the reliability and security of free space optical (FSO) communication system. We experimentally investigate a 10 Gb/s decode-and-forward (DF) relaying FSO-CDMA system and a relaying amplify-and-forward (AF) FSO-CDMA system, respectively. Bit error rates (BERs) of DF and AF relaying FSO-CDMA are measured and compared under different turbulence conditions. The experimental results show that the BER of DF relaying FSO-CDMA is one to two orders of magnitude lower than that of AF relaying FSO-CDMA when the receiving power is −5.6 dBm. However, the performance gap is decreasing with the increase of receiving power, especially when there is an interfering user. At the receiving power −2.8 dBm, two-user AF and DF relaying FSO-CDMA systems have almost the same BER. Under both weak and moderate turbulence conditions, at the receiving power −2.8 dBm, the measured BER of the eavesdropper exceeds 0.1, which is larger than the BER threshold of soft-decision forward error correction code. Hence, physical layer security of FSO relaying system can be achieved by optical coding.

Performance enhancement of multi channel multi beam FSO communication link with the application of Reed Solomon codes

The rising user needs for high speed applications and services have necessitated the requirement of a communication link that can provide the data rate comparable to optical fiber. Free Space Optical (FSO) Communication is an admired means of communication from past few years. To achieve seamless and error free transmission at high speed for heterogeneous multimedia applications at desired bit rates, novel advancements in optical communication technology are being explored along with FSO. However, several constraints such as atmospheric turbulence, uneven terrain, dynamic climatic conditions cause several nonlinearities which limit the connectivity. In this work, a multi channel multi beam FSO communication system by incorporating Reed Solomon (RS) Codes has been proposed at 30 Gbps. The Modified Gamma-Gamma model is being applied for channel turbulences. The application of Forward Error Correction (FEC) coding in the designed system offers ease of error detection and correction with improved performance at higher data rate for implementation over longer link lengths.The system performance has been evaluated for (i) Number of errors corrected, (ii) Bit Error Rate (BER), (iii) Received power, (iv) Geometric path losses and (v) Signal to Noise Ratio (SNR). At an acceptable BER of 10–9, the RS (255, 127, 129) encoded Four channel Four beam FSO communication link is effectively implemented for a distance of 3500 m with − 32.5 dBm received low optical power and 25 dB SNR.

Model-based end-to-end learning for a self-homodyne coherent system.

We investigate the statistical properties of the inherent intensity fluctuation in a low-cost and low-complexity self-homodyne coherent system employing an amplified spontaneous emission (ASE) source. The noise distribution model of the considered system is established, which is shown to be highly consistent with the experimental results for a 10 GBd 256-ary quadrature amplitude modulation (QAM) signal transmission over a 10 m duplex fiber. With the help of the proposed noise model, we then design advanced mappers and demappers. The optimized system alleviates the need for ASE bandwidth and is evaluated by applying forward error correction codes. Furthermore, we demonstrate an information rate increase of 6.67% with respect to 64-QAM.

Dual Coding Concatenation for Burst-Error Correction in Probabilistic Amplitude Shaping

We propose the use of dual coding concatenation for mitigation of post-shaping burst errors in probabilistic amplitude shaping (PAS) architectures. The proposed dual coding concatenation for PAS is a hybrid integration of conventional reverse concatenation and forward concatenation, i.e., post-shaping forward error correction (FEC) layer and pre-shaping FEC layer, respectively. A low-complexity architecture based on parallel Bose–Chaudhuri–Hocquenghem (BCH) codes is introduced for the pre-shaping FEC layer. Proposed dual coding concatenation can relax bit error rate (BER) requirement after post-shaping soft-decision (SD) FEC codes by an order of magnitude, resulting in a gain of up to 0.25 dB depending on the complexity of post-shaping FEC. Also, combined shaping and coding performance was analyzed based on sphere shaping and the impact of shaping length on coding performance was demonstrated.

Photonics based frequency hopping spread spectrum system for secure terahertz communications.

Terahertz (THz) spectrum (100 GHz-10 THz) is considered the next frontier in the design of high-speed wireless communication systems. While the high-power THz sources have commercially become available, it increases the possibility of developing THz jammers to disrupt the THz communication link. Therefore, the development of novel anti-jamming solutions is the need of the hour. In this work, we present the photonics-based THz communication system and demonstrate the frequency hopping spread spectrum (FHSS) technique which acts against the single/multi-tone jamming attack in the frequency window of 110 GHz-170 GHz. By tuning the output wavelength of the distributed feedback lasers, the THz carrier frequencies are swept back and forth within the scanning window. The frequency tuning range was measured for different scanning rates of the laser which decreases rapidly with the increase in the scanning rate. Next, we demonstrate the THz FHSS technique in a real-time communication system by transmitting a 6 Gbps NRZ signal in both wireless and THz-fiber-based links within the link distance of 1.75 m. We experimentally found that the measured bit error rate in the THz FHSS system is the time average of the measured BER for individual carrier frequencies within the hopping frequency window. By combining with the forward error correction codes and by using the tunable filter in the receiver, we believe that the proposed technique will offer a novel and compact solution against the single/multi-tone jammer for high-bit rate THz communications.