Coding Gain Research Articles

Low-Power, Phase-Slip Tolerant, Multilevel Coding for <italic>M-</italic>QAM

For a cost efficient, high capacity, coherent dense wavelength division multiplex transmission in data center interconnect applications, the number of optical interfaces should be minimized, the throughput of each modulated channel should be maximized, and the system density should be increased. These goals are supported by using high baud rates, spectrally efficient modulation, and low-power solutions. Allowing independent design of non-binary modulation and binary forward error correction (FEC) coding, bit-interleaved coded modulation (BICM) eases the system design for software-defined reach (or capacity) by combining a programmable modulation with a single binary FEC code. Unfortunately, as we demonstrate, the suboptimality of BICM implementations tends to increase both with the higher modulation order and also the higher FEC overhead. This motivates a search for alternatives to BICM. In this paper, we examine a low-power multilevel coding architecture for higher order quadrature amplitude modulation (M- QAM). Limiting ourselves to non-iterative low-power solutions, we show that two-level coding using a low-complexity convolutional code concatenated with a powerful hard decoded FEC may be an attractive approach. We demonstrate a pilot-free, phase-slip tolerant inner coding scheme with low complexity, attractive performance, and low latency. In a real-time prototype, we study the performance and implementation aspects for 64 QAM, resulting in 12.9 dB net coding gain with less than 1 W power dissipation per coded 100 G in 14 nm ASIC technology.

High performance and cost effective CO-OFDM system aided by polar code.

A novel polar coded coherent optical orthogonal frequency division multiplexing (CO-OFDM) system is proposed and demonstrated through experiment for the first time. The principle of a polar coded CO-OFDM signal is illustrated theoretically and the suitable polar decoding method is discussed. Results show that the polar coded CO-OFDM signal achieves a net coding gain (NCG) of more than 10 dB at bit error rate (BER) of 10-3 over 25-Gb/s 480-km transmission in comparison with conventional CO-OFDM. Also, compared to the 25-Gb/s low-density parity-check (LDPC) coded CO-OFDM 160-km system, the polar code provides a NCG of 0.88 dB @BER = 10-3. Moreover, the polar code can relieve the laser linewidth requirement massively to get a more cost-effective CO-OFDM system.

Generalized Multicast Multibeam Precoding for Satellite Communications

This paper deals with the problem of precoding in multibeam satellite systems. In contrast to general multiuser multiple-input-multiple-output (MIMO) cellular schemes, multibeam satellite architectures suffer from different challenges. First, satellite communications standards embed more than one user in each frame in order to increase the channel coding gain. This leads to the different so-called multigroup multicast model, whose optimization requires computationally complex operations. Second, when the data traffic is generated by several Earth stations (gateways), the precoding matrix must be distributively computed and attain additional payload restrictions. Third, since the feedback channel is adverse (large delay and quantization errors), the precoding must be able to deal with such uncertainties. In order to solve the aforementioned problems, we propose a two-stage precoding design in order to both limit the multibeam interference and to enhance the intra-beam minimum user signal power (i.e. the one that dictates the rate allocation per beam). A robust version of the proposed precoder based on a first perturbation model is presented. This mechanism behaves well when the channel state information is corrupted. Furthermore, we propose a per beam user grouping mechanism together with its robust version in order to increase the precoding gain. Finally, a method for dealing with the multiple gateway architecture is presented, which offers high throughputs with a low inter-gateway communication. The conceived designs are evaluated in a close-to-real beam pattern and the latest broadband communication standard for satellite communications.

Fading Correlations for Wireless Cooperative Communications: Diversity and Coding Gains

We theoretically analyze outage probabilities of the lossy-forward (LF), decode-andforward (DF), and adaptive decode-and-forward (ADF) relaying techniques, with the aim of characterizing the impact of the spatial and temporal correlations of the fading variations. First, the exact outage probability expressions are analytically obtained for LF, DF, and ADF relaying assuming each link suffers from statistically independent Rayleigh fading. Then, approximated, yet accurate closed-form expressions of the outage probabilities for the relaying schemes are derived. Based on the expressions, diversity and coding gains are found. The mathematical methodology for the derivation of the explicit outage probability is further extended to the case, where the account is taken of the spatial and temporal correlations of the fading variations. The diversity gains with LF, DF, and ADF are then derived in the presence of the correlations. It is found out that the three techniques can achieve full diversity, as long as the fading variations are not fully correlated. We then investigate the optimal relay location and the optimal power allocation for the three relaying techniques. It is shown that the optimal solutions can be obtained under the framework of convex optimization. It is revealed that in correlated fading, the relay should move close to the destination or allocate more transmit power to the relay for achieving lower outage probabilities, compared with the case in independent fading.

Structural adaptation of the turbo code coder and decoder for generating the transmission repeat request under conditions of uncertainty

The paper deals with the issue of enhancing the performance efficiency of wireless networks built by using the with automatic repeat request scheme for retransmission. The proposed method is based on adaptive change of polynomials of recursive systematic convolutional codes forming a part of turbo codes and aimed at enhancing their correcting properties at the expense of increasing the code limitation at each data block retransmission for the set coding rate. In this case, the decoding algorithm of turbo codes is modified in respect of using the introduced additional a priori information during the calculation of logarithmic ratios of likelihood functions or log-likelihood ratios (LLR) for each component decoder obtained during the earlier repeat requests for retransmission. The results of simulation modeling showed that the application of this technique made it possible to obtain the energy gain in coding and enhance the data transmission accuracy as compared to the fourth generation mobile communication system, such as 4G LTE-Advanced.

Evolution of Diversity Gain with and without Coding Gain in MIMO for Emerging Wireless Networks

Evolution of Diversity Gain with and without Coding Gain in MIMO for Emerging Wireless Networks

An Improved Self Adaptive Min-Sum Decoding Algorithm for Flexible Low-Density Parity-Check Decoder

In this paper, an improved self adaptive min-sum decoding algorithm for flexible low-density parity-check (LDPC) code is proposed. In the proposed algorithm, new modifications are incorporated in both the check node and variable node update process to support the irregular LDPC codes. In the check node and variable node update process of the proposed algorithm, an improved min-sum approximation and down scaling factors are adopted. These modifications result in good error correcting performance without increasing the computational complexity. Through simulations the proposed decoding algorithm is shown to exhibit better decoding performance by achieving overall FER and BER coding gain improvement of 0.31 and 0.26 dB respectively.

Construction method of QC-LDPC codes based on multiplicative group of finite field in optical communication

In order to meet the needs of high-speed development of optical communication system, a construction method of quasi-cyclic low-density parity-check (QC-LDPC) codes based on multiplicative group of finite field is proposed. The Tanner graph of parity check matrix of the code constructed by this method has no cycle of length 4, and it can make sure that the obtained code can get a good distance property. Simulation results show that when the bit error rate (BER) is 10-6, in the same simulation environment, the net coding gain (NCG) of the proposed QC-LDPC(3 780, 3 540) code with the code rate of 93.7% in this paper is improved by 2.18 dB and 1.6 dB respectively compared with those of the RS(255, 239) code in ITU-T G.975 and the LDPC(3 2640, 3 0592) code in ITU-T G.975.1. In addition, the NCG of the proposed QC-LDPC(3 780, 3 540) code is respectively 0.2 dB and 0.4 dB higher compared with those of the SG-QC-LDPC(3 780, 3 540) code based on the two different subgroups in finite field and the AS-QC-LDPC(3 780, 3 540) code based on the two arbitrary sets of a finite field. Thus, the proposed QC-LDPC(3 780, 3 540) code in this paper can be well applied in optical communication systems.

Joint source–channel coding for band‐limited backhauls in coordinated multi‐point systems

Coordinated multi-point (CoMP) transmission has been considered in the 3GPP long-term evolution advanced standard and beyond networks to improve the system throughput and coverage, particularly for cell-edge users. However, in practice the global channel state information (CSI) required by the coordinated points is usually transmitted by the band-limited backhauls, which degrades the performance of CoMP due to the erroneous backhaul transmission via the insufficient bandwidth. To address this problem, the authors propose a joint source–channel coding scheme for the backhaul transmission. They choose wavelet transform to compress the source CSI, and furthermore use irregular low-density parity-check codes to realise unequal error protection. They theoretically analyse how the joint coding affects the performance of CoMP. A trade-off between the compression ratio and channel coding gain is given. The numerical results verify that the proposed scheme can improve the performance of CoMP with band-limited backhauls.

Low-Power 400-Gbps Soft-Decision LDPC FEC for Optical Transport Networks

We present forward error correction systems based on soft-decision low-density parity check (LDPC) codes for applications in 100-400-Gbps optical transport networks. These systems are based on the low-complexity “adaptive degeneration” decoding algorithm, which we introduce in this paper, along with randomly-structured LDPC codes with block lengths from 30 000 to 60 000 bits and overhead (OH) from 6.7% to 33%. We also construct a 3600-bit prototype LDPC code with 20% overhead, and experimentally show that it has no error floor above a bit error rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-15</sup> using a field-programmable gate array (FPGA)-based hardware emulator. The projected net coding gain at a BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-15</sup> ranges from 9.6 dB at 6.7% OH to 11.2 dB at 33% OH. We also present application-specific integrated circuit synthesis results for these decoders in 28 nm fully depleted silicon on insulator technology, which show that they are capable of 400-Gbps operation with energy consumption of under 3 pJ per information bit.

Proposal and analytical investigation of optical comparator for optical and electrical converted Viterbi‐decoding scheme

A novel optical comparator is proposed for the novel Viterbi-decoding scheme, and the performance of the proposed scheme with the optical comparators is analytically investigated. The net coding gain of the proposed scheme is not degraded compared with conventional scheme, and the proposed scheme could reduce the calculation steps by a factor of ∼4/5 of the conventional scheme.

A Soft Decode–Compress–Forward Relaying Scheme for Cooperative Wireless Networks

This paper proposes a new technique for soft information relaying, which is based on a soft decode–compress–forward relay protocol. The proposed system provides a means of using distributed low-density parity-check (LDPC) coding in conjunction with higher order modulation, such as pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM), which is effective even under poor source–relay link conditions. Ordinarily, such schemes suffer from error propagation to the destination caused by incorrect decoding at the relay when the signal-to-noise ratio (SNR) on the source–relay link is low; however, our system avoids this problem by generating soft versions of the additional (parity-bearing) PAM symbols for transmission from the relay. The proposed technique of soft compression does not suffer from parity log-likelihood ratios (LLRs) converging to zero, as do many soft re-encoding techniques for turbo and LDPC codes. In the case of Gray-coded PAM/QAM signaling, we also propose a method of performing exact expectation-based soft modulation with low computational complexity. Furthermore, we propose a new model, which we refer to as the soft scalar model, for the overall source-to-destination channel encountered by the constellation symbols, and this model is used at the destination to compute LLRs for joint decoding of the distributed LDPC code. Simulation results demonstrate that the proposed scheme can provide good coding gain, diversity gain, and spectral efficiency under poor source–relay SNR conditions.

Efficient coding schemes for low‐rate wireless personal area networks

The emerging market of Internet of things has created great demand for low-cost, low-power wireless technologies. Existing IEEE 802.15.4 standard is designed for low-rate wireless personal area networks (LR-WPANs). However, current standard does not fully utilise the benefit of the code redundancy. In this study, the authors propose new coding schemes for LR-WPANs with improved coding gain. They first propose a block code based on extended Bose–Chaudhuri–Hocquenghem (BCH) code that increases the minimum Hamming distance compared with the existing code used in LR-WPANs. The computational complexity of the encoder and decoder remains about the same. In addition, by applying the extended BCH code directly to LR-WPANs, the data rate of the system can be increased without sacrificing coding performance. They further propose a tail-biting convolutional (TBC) code with optimum generator polynomials for LR-WPANs. The proposed TBC code enjoys significant performance improvement while preserving the effective code rate as well as a low decoding complexity. Simulation results validate the effectiveness of the proposed coding schemes.

Numerical Investigation of All-Optical Forward-Error-Correction Coding Scheme With Convolutional Code

In this paper, we propose an optical forward-error-correction (FEC) coding scheme with convolutional code using four-wave mixing (FWM) in a highly nonlinear fiber (HNLF) to realize an adaptive coding scheme corresponding to the signal-to-noise ratio (SNR) between nodes in photonic networks. The performance of the proposed scheme was numerically investigated for 2 11-1 pseudorandom bit sequence (PRBS) differential phase-shift keying (DPSK) modulated return-to-zero (RZ) format signals at 10 Gb/s. The optimized condition of optical XOR operations, which are the main components of the target coding scheme, is obtained for fiber length, signal wavelengths, and signal powers. Based on the optimized condition, the power penalties of the FEC coding scheme achieved are approximately 0.5 and -0.8 dB at BER 1/4 10 -9 in the cases of twoand three-input optical XOR operations, respectively, indicating that the proposed scheme obtains a net coding gain. The high-quality coded signals, which keep 5-dB degradation of the Q-factor from its maximum value of 40, are achieved with the 6.1and 6.2-dB input power tolerances for coded signals 1 and 2, respectively.

A novel construction scheme of QC-LDPC codes based on the RU algorithm for optical transmission systems

A novel lower-complexity construction scheme of quasi-cyclic low-density parity-check (QC-LDPC) codes for optical transmission systems is proposed based on the structure of the parity-check matrix for the Richardson-Urbanke (RU) algorithm. Furthermore, a novel irregular QC-LDPC(4 288, 4 020) code with high code-rate of 0.937 is constructed by this novel construction scheme. The simulation analyses show that the net coding gain (NCG) of the novel irregular QC-LDPC(4 288,4 020) code is respectively 2.08 dB, 1.25 dB and 0.29 dB more than those of the classic RS(255, 239) code, the LDPC(32 640, 30 592) code and the irregular QC-LDPC(3 843, 3 603) code at the bit error rate (BER) of 10-6. The irregular QC-LDPC(4 288, 4 020) code has the lower encoding/decoding complexity compared with the LDPC(32 640, 30 592) code and the irregular QC-LDPC(3 843, 3 603) code. The proposed novel QC-LDPC(4 288, 4 020) code can be more suitable for the increasing development requirements of high-speed optical transmission systems.

A Strategy for Improvement of Distributed Space Time Coding Gain in Cooperative Wireless Networks

A Strategy for Improvement of Distributed Space Time Coding Gain in Cooperative Wireless Networks

On the Performance of SR and FR Protocols for OSTBC-Based AF-MIMO Relay System With Channel and Noise Correlations

This paper proposes a selection relaying (SR) protocol for a cooperative multiple-input–multiple-output (MIMO) relay system that consists of a direct link between a source and a destination. The system has only receive-side channel state information (CSI) and spatially correlated MIMO channels, and the receiver nodes observe spatially correlated noise. The transmit nodes employ orthogonal space–time block codes (OSTBCs), whereas the receiver nodes employ optimum minimum mean square error (MMSE) detection. The SR protocol, which transmits via the relay only when the direct link between the source and destination is in outage, is compared with the fixed relaying (FR) protocol, which always uses the relay. By deriving novel asymptotic expressions of the outage probabilities, it is analytically shown that both protocols provide the same diversity gain. However, the coding gain (CG) of the SR protocol can be much better than that of the FR protocol. In particular, when all MIMO links have the same effective rank, irrespective of its value, the SR protocol provides better CG than the FR scheme if the target information rate is greater than $\ln_2(\mbox{3})$ bits per channel use. Simulation results support theoretical analysis and show that the SR scheme can significantly outperform the FR method, which may justify the increased complexity due to the one-bit feedback requirement in the SR protocol.

Fast Quantization Method With Simplified Rate–Distortion Optimized Quantization for an HEVC Encoder

While the rate–distortion optimized quantization (RDOQ) technique provides nontrivial coding gain in High Efficiency Video Coding (HEVC), it also involves considerable computations, whereby the complexity of quantization is significantly increased. In this paper, two schemes (the RDOQ bypass decision and the simplified level adjustment) are investigated to reduce the complexity of the quantization process in HEVC with RDOQ. The RDOQ bypass decision method initially selects the transform blocks for which the RDOQ is expected to give less/or no coding gain and enables the conventional uniform scalar quantization to be applied to these transform blocks instead of the RDOQ. The simplified level adjustment method only estimates the difference in rate–distortion costs among the candidate quantization levels to enable the encoder to select an optimal quantization level at a much reduced computational cost. Furthermore, the proposed simplified level adjustment scheme is designed so that it can be implemented in lookup tables. Experimental results show that the proposed fast method achieves 14.3% quantization complexity reduction in all intra main conditions, 15.2% in the random access main condition, and 14.9% in the low delay main condition on average with virtually no coding loss compared with the conventional quantization process with the RDOQ.

A Survey on FEC Codes for 100 G and Beyond Optical Networks

Due to the rapid increase in network traffic in the last few years, many telecommunication operators have started transitions to 100-Gb/s optical networks and beyond. However, high-speed optical networks need more efficient forward error correction (FEC) codes to deal with optical impairments, such as uncompensated chromatic dispersion, polarization mode dispersion, and nonlinear effects, and keep the bit error rate (BER) at long distances sufficiently low. To address these issues, new FEC codes, called third-generation codes, have been proposed. A majority of these codes are based on soft-decision decoders and can provide higher coding gain as compared with their predecessors. This paper presents a thorough survey of third-generation FEC codes, suitable for 100 G and beyond optical networks. Furthermore, this paper discusses the main advantages and drawbacks of each scheme and provides a qualitative categorization and comparison of the proposed schemes based on their main features, such as net coding gain and BER. Information about the complexity of each scheme is given as well.

A modified non-binary LDPC scheme based on watermark symbols in high speed optical transmission systems

We introduce a watermark non-binary low-density parity check code (NB-LDPC) scheme, which can estimate the time-varying noise variance by using prior information of watermark symbols, to improve the performance of NB-LDPC codes. And compared with the prior-art counterpart, the watermark scheme can bring about 0.25dB improvement in net coding gain (NCG) at bit error rate (BER) of 1e-6 and 36.8–81% reduction of the iteration numbers. Obviously, the proposed scheme shows great potential in terms of error correction performance and decoding efficiency.