Iterative Decoder of Channel-Polarized Multilevel Coding for Data Center Networks

In super-Nyquist wavelength division multiplexed (WDM) systems with frequency spacing smaller than the signal baudrate, the maximum-likelihood (ML) decoder in the receiver is usually introduced to compensate for intersymbol interference due to tight spectral filtering, such as polybinary shaping. After the ML decoder, symbol errors tend to propagate, causing excess continuous errors. Considering that forward error correction (FEC) is commonly introduced, the excess continuous errors degrade bit-error ratio (BER) performance after FEC, so-called post-FEC BER. In order to suppress the performance degradation, we introduce iterative decoding between the first ML decoder for polybinary shaping and the second FEC decoder in the receiver. First, we calculate BER characteristics of polybinary-shaped super-Nyquist WDM quadrature phase-shift keying (QPSK) signals. The results show that iterative decoding is effective for improving post-FEC BER performance. A lager pre-FEC BER threshold for post-FEC BER <; 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> is obtained in super-Nyquist WDM case than in the Nyquist WDM case, although a higher signal-to-noise ratio (SNR) is required. Next, we measure the BER characteristics of three-channel duobinary-shaped super-Nyquist WDM 12.5-Gbaud dual-polarization QPSK signals. The iterative decoding reduces the optical SNR penalty by 0.8 dB. A larger pre-FEC BER threshold of 3.1 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> is obtained in the duobinary-shaped super-Nyquist WDM case, compared with the threshold of 2.2 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> in the Nyquist WDM case.

Irregular LDPC codes can achieve better error rate performance than regular LDPC codes. However, irregular LDPC codes have higher error floors than regular LDPC codes. The Ordered Statistic Decoding (OSD) algorithm achieves approximate Maximum Likelihood (ML) decoding. ML decoding is effective to lower error floors. However, the OSD estimates satisfy the parity check equation of the LDPC code even the estimates are wrong. Hybrid decoder combining LLR-BP decoding algorithm and the OSD algorithm cannot also lower error floors, because wrong estimates also satisfy the LDPC parity check equation. We proposed the concatenated code constructed with an inner irregular LDPC code and an outer Cyclic Redundancy Check (CRC). Owing to CRC, we can detect wrong codewords from OSD estimates. Our CRC-LDPC code with hybrid decoder can lower error floors in an AWGN channel. In wireless communications, we cannot neglect the effects of the channel. The OSD algorithm needs the ordering of each bit based on the reliability. The Channel State Information (CSI) is used for deciding reliability of each bit. In this paper, we evaluate the Block Error Rate (BLER) of the CRC-LDPC code with hybrid decoder in a fast fading channel with perfect and imperfect CSIs where 'imperfect CSI' means that the distribution of channel and those statistical average of the fading amplitudes are known at the receiver. By computer simulation, we show that the CRC-LDPC code with hybrid decoder can lower error floors than the conventional LDPC code with hybrid decoder in the fast fading channel with perfect and imperfect CSIs. We also show that combining error detection with the OSD algorithm is effective not only for lowering the error floor but also for reducing computational complexity of the OSD algorithm.

In this contribution, KNIH algorithm and Ordered Statistic Decoding (OSD) algorithm are investigated, based on which, a novel KNIH-OSD parallel decoding scheme for LDPC codes is proposed. KNIH decoding algorithm processes certain LRPs of a received sequence, while OSD algorithm processes certain MRIPs of a received sequence. If there are too many errors in MRIPs, the OSD algorithm will fail, on the contrary, if there are too many errors in LRPs, the KNIH algorithm will fail. This contribution proposes a parallel decoding scheme based on the complementary characteristic of these two algorithms. Simulation results show that the proposed scheme is feasible and effective. Compared with OSD and KNIH algorithm, the decoding performance is improved.

In this chapter, forward error correction (FEC) techniques for optical communications are described. In Sect. 17.1, the basic concepts of FEC and its terminology are explained. The various FECs developed to date for optical communications are classified as belonging to three generations. In Sect. 17.2, the first-generation FEC represented by RS(255,239) is described. The second-generation FECs are explained in Sect. 17.3, where recently developed concatenated codes are discussed. In Sect. 17.4, the third-generation FECs, which are more powerful FECs based on soft-decision decoding, are analyzed in detail. A block turbo code and low-density parity-check (LDPC) codes showing a record NCG of around 10 dB are discussed in detail. In Sect. 17.5, we compare each generation of FEC with the Shannon limit. The ultimate NCG is discussed as a function of code rate. FEC error count and its application are discussed in Sect. 17.6.

Research in Information-Centric Networking (ICN) and Named Data Networking (NDN) has produced many protocol designs and software prototypes, but they need to be validated and evaluated by real usage on the Internet, which is also critical to the realization of the ICN/NDN vision in the long run. This article presents the first Internet-scale adaptive video streaming service over NDN, which allows regular users to watch videos using NDN technology with no software installation or manual configuration. Since mid-2019, the official NDN website [1] has started using our service to deliver its videos to Internet users over the global NDN testbed, showcasing the feasibility of NDN. We conduct real-world experiments on the NDN testbed to validate the proper implementation of the client, network, and server sides of the proposed system and also evaluate the performance of our video streaming service.

Guessing Random Additive Noise Decoding (GRAND) excels at decoding high-rate codes but struggles to decode low-rate codes with reasonable complexity. Ordered Statistics Decoding (OSD) specifically excels in decoding short codes irrespective of rates; however, OSD necessitates the use of Gaussian elimination which introduces additional time, space and computational complexity. Partial Ordered Statistics Decoding (POSD) was proposed to reduce the time, space, and computational complexity of OSD; however, the current partition-based POSD has poor decoding performance since it does not generate test error patterns across partitions. In this paper, we propose to improve the decoding performance of POSD by incorporating test error patterns inspired by GRAND methods. This work offers a trade-off between performance and complexity compared to existing decoders such as GRAND and OSD. We enhance POSD by optimizing the scheduling of Test Error Patterns (TEPs) and show that our technique can be applied to any code in a standard form. At a target BER 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−4</sup> with eBCH (128,64) the enhanced error patterns achieve more than 0.6 dB gain in performance compared to the POSD with partition-based error patterns. Moreover, at a target frame error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−5</sup> , POSD uses 10× less binary operations compared to GRAND when decoding eBCH (128,64) and RLC(128,64) codes. With BCH (127,29) and RLC(128,32), at a target frame error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−2</sup> , POSD with enhanced error patterns with a maximum number of queries (MQ) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> achieves up to a 2 dB gain to its GRAND equivalent which is using 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sup> maximum number of queries.

In this paper, soft-decision decoding is considered as an optimisation problem and a computationally efficient soft-decision decoding algorithm for block codes is developed using a compact Genetic Algorithm. The performance of this algorithm is investigated and compared with other decoding schemes. The results show the proposed algorithm gives large gains over the Generalised Minimum Distance (GMD) decoding algorithm and algebraic hard-decision decoding in flat Rayleigh fading. Further, the proposed algorithm achieves near maximum likelihood decoder (MLD) performance for the codes simulated. The complexity of this algorithm is also discussed and compared to the standard Order-l reprocessing algorithm.

We track the density of extrinsic information in iterative turbo decoders by actual density evolution, and also approximate it by symmetric Gaussian density functions. The approximate model is verified by experimental measurements. We view the evolution of these density functions through an iterative decoder as a nonlinear dynamical system with feedback. Iterative decoding of turbo codes and of serially concatenated codes is analyzed by examining whether a signal-to-noise ratio (SNR) for the extrinsic information keeps growing with iterations. We define a for the iterative decoder, such that the turbo decoder will converge to the correct codeword if the noise figure is bounded by a number below zero dB. By decomposing the code's noise figure into individual curves of output SNR versus input SNR corresponding to the individual constituent codes, we gain many new insights into the performance of the iterative decoder for different constituents. Many mysteries of turbo codes are explained based on this analysis. For example, we show why certain codes converge better with iterative decoding than more powerful codes which are only suitable for maximum likelihood decoding. The roles of systematic bits and of recursive convolutional codes as constituents of turbo codes are crystallized. The analysis is generalized to serial concatenations of mixtures of complementary outer and inner constituent codes. Design examples are given to optimize mixture codes to achieve low iterative decoding thresholds on the signal-to-noise ratio of the channel.

Transmission of 112 Gb/s dual-carrier DQPSK signal over 10 Gb/s-based WDM optical links

In this paper, the OSD algorithm is modified to perform a limited GE with O(N 3 min{R, 1− R} 3 ) complexity for an (N, K) linear block code of rate R = K/N . Index terms-decoding, soft decision decoding, ordered statistic decoding, linear codes.

Polar codes were shown to be weak at finite block lengths even under maximum-likelihood (ML) decoding. To enhance polar codes, CRC-aided polar codes were proposed. It has been shown that CRC-aided polar codes under the successive cancellation list (SCL) decoder outperform LDPC codes and turbo codes. Recently, interleaved polar (i-polar) codes were proposed. By using a new bit channel selection algorithm, i-polar codes without CRC were shown to outperform the 5G LDPC codes. However, most research on polar codes focuses on the binary case. In this paper, a new family of nonbinary i-polar codes with random constellation mapping is proposed. A recursive form for calculating the average weight enumerating function (WEF) of the nonbinary i-polar code is derived. With the random constellation mapping, the upper bound on the BLER under ML decoding depends on the WEF of the nonbinary i-polar code. Then a new channel selection algorithm is proposed based on the polarization effect and the BLER upper bound. The algorithm generates a sequence, termed the i-polar sequence (IPS). Simulation results show that the nonbinary i-polar codes with the IPS outperform the 5G LDPC codes.

In this paper, we consider a broadcast application for mobile terminals where the access points are connected to the source via a fixed network. Random Linear Network (RLN) coding is used in the fixed network to maximize its transmission rate and a wireless connection is used between the access points and the terminal. In order to reduce variations in the transmission delay and offer more flexibility to the terminal, we perform the network decoding in the terminal. We investigate the error correction capability of RLN coding using the ordered statistics decoding (OSD) algorithm. Taking into account the forward error correcting (FEC) code used on the wireless link, a product code is built by combining the FEC code and the RLN code and turbo decoded in the terminal. The proposed scheme efficiency is analyzed through its simulated and theoretical performance under additive white Gaussian noise (AWGN) and non frequency-selective block Rayleigh fading channels.

The conventional soft decision decoding (SDD) methods require various hard decision decoders (HDDs) based on different codes or re-manipulate the generator matrix by the complicated Gaussian elimination technique according to the bit reliability. This paper presents a general multi-class neural network (NN)-based decoder for the short linear block codes, where no HDD and Gaussian elimination are required once the NN is constructed. This network architecture performs multi-classification to select the messages with high occurrence probabilities and chooses the best codeword on a maximum likelihood basis. Simulation results show that the developed approach outperforms the existing deep neural network (DNN)-based decoders in terms of decoding time and bit error rate (BER). The error-correcting performance is also superior to the conventional Chase-II algorithm and is close to the ordered statistics decoding (OSD) in most cases. For Bose–Chaudhuri–Hocquenghem (BCH) codes, the SNR is improved by 1dB to 4dB as the BER is 10−4. For the (23, 12) quadratic residue (QR) code, the SNR is improved by 2dB when the BER is 10−3. The developed NN-based decoder is quite general and applicable to various short linear block codes with good BER performance.

In this paper we investigate the secure throughput of selective decode-and-forward relaying where the legitimate transmitter has no knowledge of the instantaneous channel state information with respect to neither the legitimate receiver nor the eavesdropper. Moreover, we assume a delay-critical scenario, such as in some applications of machine- to-machine communications, so that users communicate with a finite and short blocklength. The performance of direct and selective decode- and-forward cooperative communication strategies are compared. Our results show that the optimization of the blocklength, subject to a maximum length imposed by the particular application, yields important gains in terms of the secure throughput, while cooperative communications is shown to outperform direct non- cooperative transmission.

We propose a low-complexity demapping scheme for multidimensional quadrature amplitude modulation (QAM) format using a bitwise log likelihood ratio (LLR). A multidimensional modulation technique such as eight-dimensional (8D) can improve the optical signal-to-noise ratio tolerance by enlarging the minimum Euclidean distance between multidimensional symbols consisting of the plural QAM constellations. However, the optimal soft demapper for these modulation formats increases computational complexity when the formats have higher dimensions and higher order multilevel signals are involved. The rise in computation complexity comes from the fact that these formats have large number of multidimensional symbols. The proposed algorithm reduces the complexity by using the bitwise LLR of original QAM constellation. Furthermore, the proposed soft demapper is suitable for iterative decoding fed back to soft decision forward error correction, such as binary low-density parity check code, since this algorithm uses only the bitwise LLR. We experimentally verify the decoding performance for 120 GBaud 8D-16QAM of the proposed demapper and iterative decoding and demonstrate over 3900 km wavelength division multiplexed transmission.