Achievable Information Rates for Coded Modulation with Hard Decision Decoding for Coherent Fiber-Optic Systems

We analyze the achievable information rates (AIRs) for coded modulation schemes with QAM constellations with both bit-wise and symbol-wise decoders, corresponding to the case where a binary code is used in combination with a higher-order modulation using the bit-interleaved coded modulation (BICM) paradigm and to the case where a nonbinary code over a field matched to the constellation size is used, respectively. In particular, we consider hard decision decoding, which is the preferable option for fiber-optic communication systems where decoding complexity is a concern. Recently, Liga \emph{et al.} analyzed the AIRs for bit-wise and symbol-wise decoders considering what the authors called \emph{hard decision decoder} which, however, exploits \emph{soft information} of the transition probabilities of discrete-input discrete-output channel resulting from the hard detection. As such, the complexity of the decoder is essentially the same as the complexity of a soft decision decoder. In this paper, we analyze instead the AIRs for the standard hard decision decoder, commonly used in practice, where the decoding is based on the Hamming distance metric. We show that if standard hard decision decoding is used, bit-wise decoders yield significantly higher AIRs than symbol-wise decoders. As a result, contrary to the conclusion by Liga \emph{et al.}, binary decoders together with the BICM paradigm are preferable for spectrally-efficient fiber-optic systems. We also design binary and nonbinary staircase codes and show that, in agreement with the AIRs, binary codes yield better performance.Comment: Published in IEEE/OSA Journal of Lightwave Technology, 201

Improving soft FEC performance for higher-order modulations via optimized bit channel mappings

Soft forward error correction with higher-order modulations is often implemented in practice via the pragmatic bit-interleaved coded modulation paradigm, where a single binary code is mapped to a nonbinary modulation. In this paper, we study the optimization of the mapping of the coded bits to the modulation bits for a polarization-multiplexed fiber-optical system without optical inline dispersion compensation. Our focus is on protograph-based low-density parity-check (LDPC) codes which allow for an efficient hardware implementation, suitable for high-speed optical communications. The optimization is applied to the AR4JA protograph family, and further extended to protograph-based spatially coupled LDPC codes assuming a windowed decoder. Full field simulations via the split-step Fourier method are used to verify the analysis. The results show performance gains of up to 0.25 dB, which translate into a possible extension of the transmission reach by roughly up to 8%, without significantly increasing the system complexity.Comment: This paper was published in Optics Express and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-22-12-1454

Rate-Adaptive Coded Modulation for Fiber-Optic Communications

Rate-adaptive optical transceivers can play an important role in exploiting the available resources in dynamic optical networks, in which different links yield different signal qualities. We study rate-adaptive joint coding and modulation, often called coded modulation (CM), addressing non-dispersion-managed (non-DM) links, exploiting recent advances in channel modeling of these links. We introduce a four-dimensional CM scheme, which shows a better tradeoff between digital signal processing complexity and transparent reach than existing methods. We construct a rate-adaptive CM scheme combining a single low-density parity-check code with a family of three signal constellations and using probabilistic signal shaping. We evaluate the performance of the proposed CM scheme for single-channel transmission through long-haul non-DM fiber-optic systems with electronic chromatic-dispersion compensation. The numerical results demonstrate improvement of spectral efficiency over a wide range of transparent reaches, an improvement over 1 dB compared to existing methods

Terminated and Tailbiting Spatially-Coupled Codes with Optimized Bit Mappings for Spectrally Efficient Fiber-Optical Systems

We study the design of spectrally efficient fiber-optical communication systems based on different spatially coupled (SC) forward error correction (FEC) schemes. In particular, we optimize the allocation of the coded bits from the FEC encoder to the modulation bits of the signal constellation. Two SC code classes are considered. The codes in the first class are protograph-based low-density parity-check (LDPC) codes which are decoded using iterative soft-decision decoding. The codes in the second class are generalized LDPC codes which are decoded using iterative hard-decision decoding. For both code classes, the bit allocation is optimized for the terminated and tailbiting SC cases based on a density evolution analysis. An optimized bit allocation can significantly improve the performance of tailbiting SC codes codes over the baseline sequential allocation, up to the point where they have a comparable gap to capacity as their terminated counterparts, at a lower FEC overhead. For the considered terminated SC codes, the optimization only results in marginal performance improvements, suggesting that in this case a sequential allocation is close to optimal.Comment: This paper has been accepted for publication in the IEEE/OSA Journal of Lightwave Technolog

A New Class of Multiple-rate Codes Based on Block Markov Superposition Transmission

Hadamard transform~(HT) as over the binary field provides a natural way to implement multiple-rate codes~(referred to as {\em HT-coset codes}), where the code length $N=2^p$ is fixed but the code dimension $K$ can be varied from $1$ to $N-1$ by adjusting the set of frozen bits. The HT-coset codes, including Reed-Muller~(RM) codes and polar codes as typical examples, can share a pair of encoder and decoder with implementation complexity of order $O(N \log N)$. However, to guarantee that all codes with designated rates perform well, HT-coset coding usually requires a sufficiently large code length, which in turn causes difficulties in the determination of which bits are better for being frozen. In this paper, we propose to transmit short HT-coset codes in the so-called block Markov superposition transmission~(BMST) manner. At the transmitter, signals are spatially coupled via superposition, resulting in long codes. At the receiver, these coupled signals are recovered by a sliding-window iterative soft successive cancellation decoding algorithm. Most importantly, the performance around or below the bit-error-rate~(BER) of $10^{-5}$ can be predicted by a simple genie-aided lower bound. Both these bounds and simulation results show that the BMST of short HT-coset codes performs well~(within one dB away from the corresponding Shannon limits) in a wide range of code rates

New Identification and Decoding Techniques for Low-Density Parity-Check Codes

Error-correction coding schemes are indispensable for high-capacity high data-rate communication systems nowadays. Among various channel coding schemes, low-density parity-check (LDPC) codes introduced by pioneer Robert G. Gallager are prominent due to the capacity-approaching and superior error-correcting properties. There is no hard constraint on the code rate of LDPC codes. Consequently, it is ideal to incorporate LDPC codes with various code rate and codeword length in the adaptive modulation and coding (AMC) systems which change the encoder and the modulator adaptively to improve the system throughput. In conventional AMC systems, a dedicated control channel is assigned to coordinate the encoder/decoder changes. A questions then rises: if the AMC system still works when such a control channel is absent. This work gives positive answer to this question by investigating various scenarios consisting of different modulation schemes, such as quadrature-amplitude modulation (QAM), frequency-shift keying (FSK), and different channels, such as additive white Gaussian noise (AWGN) channels and fading channels. On the other hand, LDPC decoding is usually carried out by iterative belief-propagation (BP) algorithms. As LDPC codes become prevalent in advanced communication and storage systems, low-complexity LDPC decoding algorithms are favored in practical applications. In the conventional BP decoding algorithm, the stopping criterion is to check if all the parities are satisfied. This single rule may not be able to identify the undecodable blocks, as a result, the decoding time and power consumption are wasted for executing unnecessary iterations. In this work, we propose a new stopping criterion to identify the undecodable blocks in the early stage of the iterative decoding process. Furthermore, in the conventional BP decoding algorithm, the variable (check) nodes are updated in parallel. It is known that the number of iterations can be reduced by the serial scheduling algorithm. The informed dynamic scheduling (IDS) algorithms were proposed in the existing literatures to further reduce the number of iterations. However, the computational complexity involved in finding the update node in the existing IDS algorithms would not be neglected. In this work, we propose a new efficient IDS scheme which can provide better performance-complexity trade-off compared to the existing IDS ones. In addition, the iterative decoding threshold, which is used for differentiating which LDPC code is better, is investigated in this work. A family of LDPC codes, called LDPC convolutional codes, has drawn a lot of attentions from researchers in recent years due to the threshold saturation phenomenon. The IDT for an LDPC convolutional code may be computationally demanding when the termination length goes to thousand or even approaches infinity, especially for AWGN channels. In this work, we propose a fast IDT estimation algorithm which can greatly reduce the complexity of the IDT calculation for LDPC convolutional codes with arbitrary large termination length (including infinity). By utilizing our new IDT estimation algorithm, the IDTs for LDPC convolutional codes with arbitrary large termination length (including infinity) can be quickly obtained

On hard-decision forward error correction with application to high-throughput fiber-optic communications

The advent of the Internet not only changed the communication methods significantly, but also the life-style of the human beings. The number of Internet users has grown exponentially in the last decade, and the number of users exceeded 3.4 billion in 2016. Fiber links serve as the Internet backbone, hence, the fast grow of the Internet network and the sheer of new applications is highly driven by advances in optical communications. The emergence of coherent optical systems has led to a more efficient use of the available spectrum compared to traditional on-off keying transmission, and has made it possible to increase the supported data rates. To achieve high spectral efficiencies and improve the transmission reach, coding in combination with a higher order modulation, a scheme known as coded modulation (CM), has become indispensable in fiber-optic communications. In the recent years, graph-based codes such as low-density parity-check codes and soft decision decoding (SDD) have been adopted for long-haul coherent optical systems. SDD yields very high net coding gains but at the expense of a relatively high decoding complexity, which brings implementation challenges at very high data rates. Hard decision decoding (HDD) is an appealing alternative that reduces the decoding complexity. This motivates the focus of this thesis on forward error correction (FEC) with HDD for high-throughput, low power fiber-optic communications.In this thesis, we start by studying the performance bounds of HDD. In particular, we derive achievable information rates (AIRs) for CM with HDD for both bit-wise and symbol-wise decoding, and show that bit-wise HDD yields significantly higher AIRs. We also design nonbinary staircase codes using density evolution. Finite length simulation results of binary and nonbinary staircase codes corroborate the conclusions arising from the AIR analysis, i.e., for HDD binary codes are preferable. Then, we consider probabilistic shaping. In particular, we extend the probabilistic amplitude shaping (PAS) scheme recently introduced by B\uf6cherer et al. to HDD based on staircase codes. Finally, we focus on new decoding algorithms for product-like codes to close the gap between HDD and SDD, while keeping the decoding complexity low. In particular, we propose three novel decoding algorithms for product-like codes based on assisting the HDD with some level of soft information. The proposed algorithms provide a clear performance-complexity tradeoff. In particular, we show that up to roughly half of the gap between SDD and HDD can be closed with limited complexity increase with respect to HDD

LDPC concatenated space-time block coded system in multipath fading environment: Analysis and evaluation

Irregular low-density parity-check (LDPC) codes have been found to show exceptionally good performance for single antenna systems over a wide class of channels. In this paper, the performance of LDPC codes with multiple antenna systems is investigated in flat Rayleigh and Rician fading channels for different modulation schemes. The focus of attention is mainly on the concatenation of irregular LDPC codes with complex orthogonal space-time codes. Iterative decoding is carried out with a density evolution method that sets a threshold above which the code performs well. For the proposed concatenated system, the simulation results show that the QAM technique achieves a higher coding gain of 8.8 dB and 3.2 dB over the QPSK technique in Rician (LOS) and Rayleigh (NLOS) faded environments respectively