Net Coding Gain Research Articles

Feature of the forward error correction constructions for optical transport networks

Due to the rapid increase of network traffic in the last few years, many telecommunication operators have started transitions to 100G optical networks and beyond. However, high speed optical networks need more efficient Forward Error Correction (FEC) codes to deal with the optical impairments. Forward error correction is widely used in optical communications to improve error correction and extend optical transmission distance. It is also used to reduce optical transmitter power and system costs. In response to the rapid growth of optical communications, the ITU-T has started researching FEC coding and has recommended ITU-T G.709 and G.975.1. As optical transmission systems evolve towards longer transmission distance, greater capacity, and speeds of 100G and beyond a variety of unwanted effects are seriously affecting smooth evolution. In optical transport network, FEC is getting more and more important as spectral efficiency is increasing. As 100G system is commercialized, there are some trends in the evolution of FEC, for example overhead is increased from 7% to 20% or even more. High-performance FEC codes are therefore being developed so that higher net coding gain (NCG) and better error correction can be achieved. The Optical Internetworking Forum (OIF) suggests that soft-decision forward-error correction (SD-FEC) with a redundancy of 20% and beyond be used in a 100G DWDM coherent system. The use of advanced modulation formats is a promising solution for attaining such high data rates in optical networks. However, as a signal constellation grows in size, so does the optical signal to signal-to-noise ratio it requires to achieve a certain bit error rate (BER). This will degrade the error correction capability. Decoding is moving from hard to soft. Vendors are developing their own advanced codes instead of using codes recommended by ITU-T. Because different application systems have different decoding performance, latency, power and cost requirements, FEC systems with various transmission overhead, implementation complexity, burst-error correction ability and error floor are available in today’s market. Soft-decision FEC often uses turbo product codes and low density parity check (LDPC) codes. In research area, new codes such as LDPC codes and their different varieties are introduced into optical communication. Optimized codeword structure and decoding algorithm that provides low BER. LDPC codes can be very powerful, but their practical implementation for optical communications links at ultra-high data rates remains a challenge since the decoding of the code requires soft-decision bits about the received bits. A family of structured codes known as quasi-cyclic LDPC codes, whose common structural properties can be exploited by unified encoding and decoding architectures to reduce the complexity in implementation.

Generalized weighted bit-flipping LDPC decoding for asymmetric optical channels

Efficient low-complexity and low-latency forward error correction (FEC) decoding is vital in high-speed optical receivers. The weighted bit-flipping (WBF) decoding algorithm is a low-complexity and high-performance iterative decoder for low-density parity-check (LDPC) codes, devised for symmetric Gaussian channels. In this paper, we present a generalization of the WBF algorithm and its variants to discrete and continuous asymmetric optical channels which have signal-dependent noises. We have employed a fully analytical approach to derive the generalized WBF decoders, and show that they can achieve a net coding gain within 0.5 dB of that of the soft-decision near-optimal decoding.

Variable-Rate VLSI Architecture for 400-Gb/s Hard-Decision Product Decoder

Variable-rate transceivers, which adapt to the conditions, will be central to energy-efficient communication. However, fiber-optic communication systems with high bit-rate requirements make design of flexible transceivers challenging, since additional circuits needed to orchestrate the flexibility will increase area and degrade speed. We propose a variable-rate VLSI architecture of a forward error correction (FEC) decoder based on hard-decision product codes. Variable shortening of component codes provides a mechanism by which code rate can be varied, the number of iterations offers a knob to control the coding gain, while a key-equation solver module that can swap between error-locator polynomial coefficients provides a means to change error correction capability. Our evaluations based on 28-nm netlists show that a variable-rate decoder implementation can offer a net coding gain (NCG) range of 9.96-10.38dB at a post-FEC bit-error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-15</sup> . The decoder achieves throughputs in excess of 400Gb/s, latencies below 53ns, and energy efficiencies of 1.14pJ/bit or less. While the area of the variable-rate decoder is 31% larger than a decoder with a fixed rate, the power dissipation is a mere 5% higher. The variable error correction capability feature increases the NCG range further, to above 10.5dB, but at a significant area cost.

Investigation for achievable NCG of optical FEC coding with convolutional code using optical XOR gates based on four‐wave mixing in highly non‐linear fibre

This study has given the investigation for achievable net coding gain (NCG) of optical forward error correction (FEC) coding scheme with convolutional code to control the received sensitivity following a required signal-to-noise ratio in the communication channel. The achievable NCG is obtained from the difference between the upper bound NCG and the power penalty of the optical exclusive-OR (XOR) gate, which is based on a four-wave mixing in highly non-linear fibre. The upper bound NCG was analytically derived by calculating error probability of optimal convolutional code, and the power penalty was numerically derived by comparing bit-error rates between with and without the optical FEC coding. To confirm the feasibility for achieving the highest NCG, the optimal operating condition of the optical XOR gate is experimentally evaluated to minimise their power penalty. A 0.5 dB power penalty was obtained at BER = 10 − 9 under the optimised condition with 223−1 pseudo-random binary sequence differential phase-shift keying-modulated return to zero signal at 10 Gbps.

Performance-Complexity Tradeoffs of Concatenated FEC for Higher-Order Modulation

Multilevel coding (MLC) is compared with bit-interleaved coded modulation (BICM) from a performance-versus-complexity standpoint. In both approaches, complexity-optimized error-reducing low-density parity-check inner codes are designed for concatenation with an outer hard-decision code, for various modulation orders. The codes are designed to achieve various points on the Pareto frontier characterizing the performance-complexity tradeoff. Computer simulations of the resulting codes reveal that MLC not only provides significant advantages compared with BICM, but also outperforms several existing MLC and BICM proposals. At 25% overhead, MLC provides a net coding gain of up to 12.8 dB with 16-QAM (1.0 dB from the constrained Shannon limit), a net coding gain of up to 13.6 dB with 64-QAM (1.2 dB from the constrained Shannon limit), and a net coding gain of up to 14 dB with 256-QAM (1.65 dB from the constrained Shannon limit), all with reasonable decoding complexity.

A new construction method of QC-LDPC codes with low error floor based on EETS and Zig-Zag

Aiming at the problem that quasi-cyclic low density parity check (QC-LDPC) codes may have the error floor in the high signal to noise ratio (SNR) region, a new construction method of the QC-LDPC codes with the low error floor is proposed. The basic matrix of the method is based on the progressive edge growth (PEG) algorithm and the improved eliminate elementary trapping sets (EETS) algorithm so as to eliminate the elementary trapping sets in the basic matrix, then the Zig-Zag method is used to construct the cyclic shift matrix which is used to extend the basic matrix in order to construct the parity check matrix. The method not only can improve the error floor in the high SNR region, but also can flexibly design the code length and code rate. The simulation results show that at the bit error rate of 10−6, the PEG-trapping-Zig-Zag (PTZZ)-QC-LDPC(3024,1512) codes with the code rate of 0.5, compared with the PEG-Zig-Zag (PZZ)-QC-LDPC(3024,1512) codes and the PEG-QC-LDPC(3024,1512) codes, can respectively improve the net coding gain of 0.1 dB and 0.16 dB. The difference among the bit error rate performance curves will become better with the increase of the SNR. In addition, the PTZZ-QC-LDPC(3024,1512) codes have no error floor above the SNR of 2.2 dB.

Design of irregular QC-LDPC code based multi-level coded modulation scheme for high speed optical communication systems

In this paper, we focus on the design of irregular QC-LDPC code based multi-level coded modulation (MLCM) scheme by jointly optimizing the component code rate and the degree distribution of the irregular QC-LDPC component code. Firstly, the sub-channel capacities of MLCM systems is analyzed and discussed, based on which the optimal component code rate can be obtained. Secondly, an extrinsic information transfer chart based two-stage searching algorithm is proposed to find the good irregular QC-LDPC code ensembles with optimal component code rates for their corresponding sub-channels. Finally, by constructing the irregular QC-LDPC component codes from the designed ensembles with the aim of possibly enlarging the girth and reducing the number of the shortest cycles, the designed irregular QC-LDPC code based 16QAM and 64QAM MLCM systems can achieve 0.4dB and 1.2dB net coding gain, respectively, compared with the recently proposed regular QC-LDPC code based 16QAM and 64QAM MLCM systems.

Multilevel Coding With Spatially Coupled Repeat-Accumulate Codes for High-Order QAM Optical Transmission

We propose multilevel coding (MLC) with spatially coupled codes to increase the net coding gain (NCG) and reduce the power consumption of forward error correction (FEC) codes in high-order quadratic-amplitude modulation (QAM) optical transmissions. We optimized the degree distribution of the spatially coupled repeat-accumulate (SC-RA) codes by using density evolution to enhance the effect of spatial coupling with a limited code length. We constructed multilevel codes with the SC-RA codes and investigated their performance in numerical simulations. NCGs of 12.5, 13.2, and 13.7 dB were obtained for 16, 64, and 256 QAM. We found that MLC is more efficient in terms of circuit size and computational complexity than the conventional FEC configuration of bit-interleaved coded modulation (BICM). Moreover, its efficiency tends to increase as the modulation order increases. Our estimates suggest that the power consumed in the FEC process could be reduced to about half for 16 QAM, 35% for 64 QAM, and 15% for 256 QAM compared with when BICM is used to obtain similar NCG values.

Block Markov Superposition Transmission of BCH Codes With Iterative Erasures-and-Errors Decoders

In this paper, we present the block Markov superposition transmission of BCH (BMST-BCH) codes, which can be constructed to obtain a very low error floor. To reduce the implementation complexity, we design a low complexity iterative sliding-window decoding algorithm, in which only binary and/or erasure messages are processed and exchanged between processing units. The error floor can be predicted by the proposed genie-aided lower bounds, while the waterfall performance can be analyzed by the density evolution method. To evaluate the error floor of the constructed BMST-BCH codes at a very low bit error rate (BER) region, we propose a fast simulation approach. Numerical results show that, at a target BER of $10^{-15}$ , the proposed BMST-BCH code with hard-decision can achieve a net coding gain (NCG) of 10.55 dB with 25% overhead, while a soft-decision design can yield an NCG of 10.74 dB. The construction of BMST-BCH codes is flexible to trade off latency against performance at all overheads of interest and may find applications in optical transport networks as an attractive candidate.

Polar-Coded MIMO FSO Communication System Over Gamma-Gamma Turbulence Channel With Spatially Correlated Fading

In this paper, for the first time to the best of our knowledge, a polar-coded multiple-input multiple-output (MIMO) free space optical (FSO) communication system is proposed to combat turbulence-induced fading. Here, the spatially correlated fading, which dominates the MIMO FSO system aggravation, is taken into consideration in this polar-coded MIMO FSO system. To evaluate our scheme, the ergodic capacity of the gamma-gamma modeled MIMO FSO turbulence channel with and without spatially correlated fading is studied. The results of ergodic capacity and Monte Carlo simulation show that the polar-coded multiple photodetector scheme can effectively mitigate the fading induced by turbulence, and the polar-coded multiple optical sources scheme is robust to the spatially correlated turbulence. Further, more than 20 dB net coding gain (NCG) is achieved for the polar-coded MIMO FSO scheme in a strong turbulence condition with spatially correlated fading. Compared with low density parity check codes, polar codes achieve a 0.4–1.6 dB NCG improvement under a strong turbulence condition with and without spatially correlated fading, which verifies that our scheme is a promising candidate for combating turbulence-induced fading.

Approaching Miscorrection-Free Performance of Product Codes With Anchor Decoding

Product codes (PCs) protect a 2-D array of bits using short component codes. Assuming transmission over the binary symmetric channel, the decoding is commonly performed by iteratively applying bounded-distance decoding to the component codes. For this coding scheme, undetected errors in the component decoding-also known as miscorrections-significantly degrade the performance. In this paper, we propose a novel iterative decoding algorithm for PCs which can detect and avoid most miscorrections. The algorithm can also be used to decode many recently proposed classes of generalized PCs, such as staircase, braided, and half-product codes. Depending on the component code parameters, our algorithm significantly outperforms the conventional iterative decoding method. As an example, for double-error-correcting Bose-Chaudhuri-Hocquenghem component codes, the net coding gain can be increased by up to 0.4 dB. Moreover, the error floor can be lowered by orders of magnitude, up to the point where the decoder performs virtually identical to a genie-aided decoder that avoids all miscorrections. We also discuss post-processing techniques that can be used to reduce the error floor even further.

A 9.52 dB NCG FEC Scheme and 162 b/Cycle Low-Complexity Product Decoder Architecture

Powerful Forward Error Correction (FEC) schemes are used in optical communications to achieve bit-error rates below $10^{-15}$. These FECs follow one of two approaches: concatenation of simpler hard-decision codes or usage of inherently powerful soft-decision codes. The first approach yields lower Net Coding Gains (NCGs), but can usually work at higher code rates and have lower complexity decoders. In this work, we propose a novel FEC scheme based on a product code and a post-processing technique. It can achieve an NCG of 9.52~dB at a BER of $10^{-15}$ and 9.96~dB at a BER of $10^{-18}$, an error-correction performance that sits between that of current hard-decision and soft-decision FECs. A decoder architecture is designed, tested on FPGA and synthesized in 65 nm CMOS technology: its 164 bits/cycle worst-case information throughput can reach 100 Gb/s at the achieved frequency of 609~MHz. Its complexity is shown to be lower than that of hard-decision decoders in literature, and an order of magnitude lower than the estimated complexity of soft-decision decoders.

Low-Complexity Concatenated LDPC-Staircase Codes

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

A two-stage coded modulation scheme based on the 8-QAM signal for optical transmission systems

A novel two-stage coded modulation (TSCM) scheme based on the 8-QAM signal is proposed. In the proposed scheme, three bits in the same symbol are protected by different codes in order to fully utilize 8-QAM’s ring characteristic and obtain the more coding gain in optical transmission systems. The two simulation experiments with two groups of quasi-cyclic low-density parity-check (QC-LDPC) codes are performed. The simulation results show that the proposed scheme, compared with the traditional parallel independent scheme which has similar code-rate, can bring about 0.5dB and 0.1dB net coding gain (NCG) respectively at the bit error ratio (BER) of 10-6. In addition, the applied QC-LDPC codes need less times of iterations and have low error floor. The proposed scheme can implement the transmission without time delay, and the number of addition operations is also only 2/3 of the traditional scheme while calculating the log-likelihood ratio (LLR) algorithm of a symbol. Therefore, the proposed TSCM scheme combined with the QC-LDPC codes has the better comprehensive performance and can better be suitable for high-speed optical transmission systems.

A Novel Construction of QC-LDPC Codes Based on Combinatorial Mathematics

In order to solve the problems of high coding complexity and inflexible code length selection in quasi-cyclic low-density Parity-check (QC-LDPC) codes, a deterministic structure is proposed based on the perfect cyclic difference sets. The number of shifts of base matrix can be obtained by a simple addition and subtraction. Because of the special structure of the base matrix and the perfect cyclic difference sets, it saves the storage space and reduces the complexity of the hardware implementation. The girth is at least six and the code-length and code-rate can be selected flexibly. Simulation results demonstrate that the Net Coding Gain of the irregular PCDS-QC-LDPC(2680, 1340) code based on perfect cyclic difference sets has respectively improved 0.13dB and 0.32dB than the code based on PEG-QC-LDPC(2680,1340) and array dispersion and masking AD-MASK-QC-LDPC(2680,1340) with the rate of 0.5 and the bit error rate of 10-6 by using the sum-product algorithm iterative decoding in the additive white Gaussian channel.

Low-Complexity Soft-Decision Concatenated LDGM-Staircase FEC for High-Bit-Rate Fiber-Optic Communication

A concatenated soft-decision forward error correction (FEC) scheme consisting of an inner low-density generator-matrix (LDGM) code and an outer staircase code is proposed. The soft-decision LDGM code is used for error reduction, while the majority of bit errors are corrected by the low-complexity hard-decision staircase code. Decoding complexity of the concatenated code is quantified by a score based on the number of edges in the LDGM code Tanner graph, the number of decoding iterations, and the number of staircase code decoding operations. The inner LDGM ensemble is designed by solving an optimization problem, which minimizes the product of the average node degree and an estimate of the required number of decoding iterations. A search procedure is used to find the inner and outer code pair with lowest complexity. The design procedure results in a Pareto-frontier characterization of the tradeoff between net coding gain and complexity for the concatenated code. Simulations of code designs at $\text{20}\%$ overhead showed that the proposed scheme achieves net coding gains equivalent to existing soft-decision FEC solutions, with up to $\text{57}\%$ reduction in complexity.

Experimental demonstration of polar coded IM/DD optical OFDM for short reach system

In this paper, we propose a novel polar coded intensity modulation direct detection (IM/DD) optical orthogonal frequency division multiplexing (OFDM) system for short reach system. A method of evaluating the channel signal noise ratio (SNR) is proposed for soft-demodulation. The experimental results demonstrate that, compared to the conventional case, ∼9.5 dB net coding gain (NCG) at the bit error rate (BER) of 1E-3 can be achieved after 40-km standard single mode fiber (SSMF) transmission. Based on the experimental result, (512,256) polar code with low complexity and satisfactory BER performance meets the requirement of low latency in short reach system, which is a promising candidate for latency-stringent short reach optical system.

Low-Power, Phase-Slip Tolerant, Multilevel Coding for &lt;italic&gt;M-&lt;/italic&gt;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.

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.