Distribution Matcher Research Articles

Nonlinear-tolerant two-dimensional distribution matcher scheme for probabilistic shaping.

This Letter proposes a nonlinear-tolerant two-dimensional distribution matcher (2D-DM) scheme. It removes the corner points of probabilistically shaped quadrature amplitude modulation (QAM) to obtain better nonlinear tolerance. Because the remaining number of points is not a power of 2, we propose to divide constellation points into different layers and symbols. Then, the proposed 2D-DM performs matching using one-dimensional shapers, which generates the in-phase and quadrature components of QAM together. In fact, it realizes two-dimensional shapers from one-dimensional shapers. Simulation results show that two-dimensional shapers generated by the proposed 2D-DM have higher tolerance to power amplifier nonlinearity and fiber nonlinearity compared to one-dimensional shapers.

FPGA based modified multi-repeat distribution matcher for probabilistic amplitude shaping

The technique of probabilistic amplitude modulation, based on distribution matching, has garnered considerable attention in recent years as a means to enhance spectral efficiency and diminish the constellation energy of coded modulation. This paper introduces the implementation of Probabilistic Amplitude Modulation (PAS) using a Modified Multi-Repeat Distribution Matcher (MMRDM) on a Field Programmable Gate Array (FPGA). The Modified Multiple Repetition Distribution Matcher (MMRDM) is integrated into a 2×2 Multiple Input Multiple Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) system, realized through the Xilinx System Generator (XSG). Simple Zero-Forced and Minimum Mean Squared Error (MMSE) equalizers are applied to the receiver for signal detection across the MIMO channel. The system incorporates enhanced security through chaos-based scrambling with 16 and 64 Quadrature Amplitude Modulation (QAM). VHDL code files for this system are generated for the Xilinx Kintex-7 (xc7k325t-3fbg676) for hardware implementation. Performance evaluation includes an assessment of required storage capacity, complexity, and bit error rate (BER). Using Vivado 2017.4, the system is successfully routed with resource utilization, for example, 0.67% Block RAM (BRAM), 68.6% Look-Up Tables (LUT), 83% DSP 48s, and 1.5% registers for 64-QAM uniform modulation. Similarly, for 64-QAM 10 level (shaper output 60 bit) shaped modulation, the resource utilization is 0.67% BRAM, 68.8% LUT, 83% DSP 48s, and 1.6% registers on the specified device. Simulation results demonstrate an improvement in the net shaping gain of approximately (2-4 dB) at 1×10^(-4) for different equalizer cases compared to uniform QAM, along with a notable reduction in required storage capacity and computational complexity.

16QAM OFDM-PON based on polar code and CCDM joint chaotic encryption.

A new optical transmitting scheme based on chaotic constant component distribution matcher (CCDM) and Polar coding was proposed. The data is first encrypted by Polar coding using a five-dimensional chaotic sequence. Then the encrypted data is divided into two paths to perform chaotic CCDM encryption operations with different schemes. Finally, the two channels are merged, and the subcarriers are scrambled. The transmission experiment of 16QAM-OFDM signal on 2 km seven-core fiber is conducted to verify the scheme's feasibility. The experimental results show that the received optical power of all ONUs is less than -15dBm when the BER of all ONUs is reduced to less than 10-3. In addition, the key space of the proposed system reaches 1085, and the security performance is further enhanced. The advantages of BER and safety performance make this two-path chaotic encrypted OFDM-PON with an optimistic application prospect in the current optical transmission systems.

Two-Level LDPC-Coded Modulation With Probabilistic Shaping

In this letter, we propose a new coded modulation scheme, namely two-level coding with probabilistic shaping, for transmission with higher spectral efficiency in future 6G communications. At the transmitter, a distribution matcher for probabilistic shaping is concatenated with two-level coding, where the first level is designed based on bit-interleaved coded modulation while the second level is left uncoded. At the receiver, a two-stage decoding is performed prior to shaping decoding. A labeling strategy is optimized to get good performance for the first-level coding. Meanwhile, labels of signal subsets are sign-bit decomposable to accommodate uniform check bits. Numerical results show that, for 256-QAM, performances of the proposed scheme are 0.7~1.4 dB better than uniform BICM at various transmission rates, while the required LDPC code length is shorter by 50%.

Probabilistic constellation shaping-aided underwater acoustic communication with vector approximate message passing iterative equalization.

A probabilistic constellation shaping (PCS)-aided single-carrier transceiver is proposed to improve spectral efficiency for underwater acoustic (UWA) communications. At the transmitter, the information bits are input into a distribution matcher followed by a systematic binary encoder, which yields a sequence of sign bits with a uniform distribution and a sequence of amplitude bits with a non-uniform distribution. Based on these two sequences, the PCS is then realized by mapping coded bits onto a quadrature amplitude modulation constellation. At the receiver, an improved frequency-domain turbo equalizer based on the vector approximate message passing (VAMP) is proposed for the PCS-UWA communication system to eliminate the multipath interference. It exploits the a priori symbol probability information benefiting from the PCS at the beginning of the turbo iteration and over the self-iteration of the VAMP soft equalizer, improving the symbol detection performance. Finally, the first experimental demonstration of a deep-sea PCS-UWA communication system and numerical simulation of shallower water are presented. The experimental results reveal the PCS-UWA communication system significantly outperforms traditional systems with no PCS. Also, the proposed receiver is superior to the classical adaptive turbo equalizer based on the improved proportionate normalized least mean square algorithm even with data reuse.

Probabilistic Shaping for Trellis-Coded Modulation With CRC-Aided List Decoding

This paper applies probabilistic amplitude shaping (PAS) to cyclic redundancy check (CRC)-aided tail-biting trellis-coded modulation (TCM). CRC-TCM-PAS produces practical codes for short block lengths on the additive white Gaussian noise (AWGN) channel. In the transmitter, equally likely message bits are encoded by a distribution matcher (DM) generating amplitude symbols with a desired distribution. A CRC is appended to the sequence of amplitude symbols, and this sequence is then encoded and modulated by TCM to produce real-valued channel input signals. This paper proves that the sign values produced by the TCM are asymptotically equally likely to be positive or negative. The CRC-TCM-PAS scheme can thus generate channel input symbols with a symmetric capacity-approaching probability mass function. The paper provides an analytical upper bound on the frame error rate of the CRC-TCM-PAS system over the AWGN channel. This FER upper bound is the objective function used for jointly optimizing the CRC and convolutional code. Additionally, this paper proposes a multi-composition DM, which is a collection of multiple constant-composition DMs. The optimized CRC-TCM-PAS systems achieve frame error rates below the random coding union (RCU) bound in AWGN and outperform the short-blocklength PAS systems with various other forward error correction codes studied in Coşkun et al. (2019).

A Novel Polar-Coded Probabilistic Shaping Scheme for Optical DMT Interconnection

A novel bit-oriented probabilistic shaping (PS) scheme based on polar-coded bit weight reconstruction (BWR) is proposed and experimentally demonstrated in an intensity modulation and direct-detection optical discrete multi-tone (DMT) interconnection. The BWR is utilized to enhance the weight of bit ‘0’ by dynamic frozen bits shaping in a systematic-like polar encode processing. Compared with the probability-oriented PS schemes employing distribution matcher (DM) with high computational complexity and PS redundancy, and the symbol-oriented ones based on many-to-one mapping with overlapped symbol demapping difficulty, the proposed bit-oriented PS scheme is with the advantages of relatively lower complexity decoder and shaping redundancy-free profile. The experimental results show that 1.34-dB improvement for receiver power sensitivity and 2.52-dB enhancement for systematic tolerance to optical fiber nonlinear effect can be obtained by the polar-coded PS-16QAM DMT signals compared with the unshaped ones in a 5-km optical DMT interconnection system.

Probabilistically Shaped PAM-8 Transmission With Simplified Volterra Equalizer

Intensity-modulation direct-detection (IM/DD) probabilistically shaped (PS) 8-level pulse-amplitude modulation (PAM) signal is promising for high-speed intra-data-center networks. However, the challenges of a PS-PAM-8 transmission system are complicated distribution matcher (DM) and nonlinear equalizer. In this work, we propose a simple PS-PAM-8 transmission system, where the probabilistic amplitude shaping (PAS) encoder consists of an energy-level-assigned (ELA)-based DM and a low-density parity-check (LDPC) encoder. In the ELA-based DM, a simple lookup table is designed to realize an approximate bilateral Maxwell-Boltzmann distribution by assigning energy levels to various symbols. Consequently, the DM encoded bits are used as the amplitude bits, and DM label bits and LDPC check bits are designated as sign bits to implement PAS encoding. In addition, a simplified Volterra equalizer (SVE) is introduced to eliminate the inter-symbol interference and improve the receiver sensitivity of PS-PAM-8 signal, where the SVE only includes the 2-order kernel to reduce its complexity. We experimentally demonstrated the proposed PS-PAM-8 scheme and verified its outperformance over uniform PAM-8 signal in the back-to-back and 2-km standard single mode fiber (SSMF) transmission. Compared to the conventional linear equalizer, the SVE contributes approximate 1-dB improvement of the receiver sensitivity in the PS-PAM-8 2-km SSMF transmission, for the error-free performance of post forward error correction bit error ratio.

On Optimization and Analysis of Enumerative Sphere Shaping for Short Blocklengths

Enumerative sphere shaping (ESS) has drawn considerable attention in recent years, yielding a practical solution for the application of probabilistic shaping in the short-blocklength regime. However, ESS suffers from some energy-efficiency degradation for binary transmission, because it orders sequences lexicographically. In this work, we propose the optimum ESS (OESS), as an optimized version of ESS, which can always achieve the lowest average energy at any blocklength. We conduct a comprehensive study on ESS and OESS in terms of energy efficiency, distribution, rate loss and practical performance. Moreover, we propose to use the reverse trellis to obtain the sequence energy distribution of ESS and OESS. Numerical analysis shows that OESS leads to better energy efficiency, as well as more Maxwell-Boltzmann-like distributions compared with ESS, yielding considerably lower rate loss. The effectiveness of OESS is verified by the Monte-Carlo simulation in the linear additive white Gaussian noise channel, and an experimental transmission in a single sideband discrete-Fourier-transform spread discrete multi-tone system. Compared with conventional constant composition distribution matcher, both ESS and OESS performs remarkably better for the short blocklengths. Moreover, OESS achieves observable gains over ESS for ultrashort blocklengths of 20 and 40.

Parallel Distribution Matcher Base on CCDM for Probabilistic Amplitude Shaping in Coherent Optical Fiber Communication

As a typical high-order modulation format optimization technology, constellation probability shaping enhances generalized mutual information (GMI) by optimizing the probability distribution of each constellation point of the signal. It can improve the transmission capacity of the same order M Quadrature Amplitude Modulation (QAM) signal under the condition of limited average transmission power, and further narrow the gap with the Shannon limit capacity. The distribution matcher is a key part of constellation probability shaping since it not only ensures the one-to-one mapping of input and output sequences but also realizes the function of probability shaping. The constant composition distribution matcher (CCDM) structure is a widely utilized distribution matcher in the current probability shaping technology. Based on CCDM, a parallel distribution matcher scheme is proposed in this paper. It has a lower rate loss than CCDM for short output lengths (n is less than 100). Block lengths can be reduced by up to 30% with the same rate loss. When the GMI is the same as for the probability shaping (PS) 64QAM signal using CCDM, the OSNR required by the PS-64QAM signal using this scheme can be enhanced by 0.12dB, the block length can be reduced by 40%, and the transmission distance in a standard single-mode fiber can be slightly extended.

Rate-Adaptive Concatenated Multi-Level Coding With Novel Probabilistic Amplitude Shaping

This paper proposes a new probabilistic amplitude shaping (PAS) approach for concatenated two-level multi-level coding (MLC). The proposed system is based on a concatenated forward error correction (FEC) scheme where outer codes are serially concatenated with inner two-level MLC. This concatenated two-level MLC scheme has recently been shown to have a potential for achieving better performance-complexity trade-offs than the conventional bit-interleaved coded modulation (BICM). Meanwhile, PAS has recently been demonstrated to offer remarkable performance gains as well as rate adaptivity. However, the majority of existing works on PAS assume the use of the binary reflected Gray code as a bit-labeling, and its application to coded modulation schemes with other bit-labelings, such as two-level MLC, may not be straightforward. In this paper, we devise a bit-labeling scheme and propose a new PAS structure for an efficient integration of PAS with two-level MLC systems. More specifically, we propose to generate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">signed</i> amplitude symbols with the distribution matcher (DM) for maximizing both coding and shaping gains achieved by two-level MLC and PAS, respectively, while the conventional PAS generates <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unsigned</i> amplitude symbols. It is demonstrated by simulation results that, with 256QAM and inner polar codes, the proposed two-level MLC with PAS simultaneously offers 75% reduction in the number of required inner encoding and soft-decision (SD) decoding operations for given outer and inner FEC code lengths, and up to 0.3 dB performance gain over the conventional PAS scheme.

Performance enhanced probabilistically shaped PAM4 signal based on nonlinear differential coding for IM/DD system

In this paper, the probabilistically shaped pulse amplitude modulation (PS-PAM) signal is proposed in intensity modulation and direct detection (IM/DD) system. For the traditional shaping scheme with constant composition distribution matcher (CCDM), there are several problems that high-precision algorithm for long block coding, the loss of information rate for short block coding. In addition, it can increase nonlinear interference. In order to reduce computational complexity and alleviate the influence of nonlinear interference on the system, the nonlinear differential coding (NLDC) scheme is used to realize PS, which can be better integrated with the cost-effective optical access network. This paper evaluates seven shaping spectrums obtained by different NLDC coding coefficients. As the coding coefficient increases, the performance of the system gradually improves. Moreover, this paper proposed the machine learning includes neural network (NN) and improved K-means clustering algorithm at the receiver. The results show that the PS-PAM4 signal is significantly better than the ordinary PAM4 signal in improving the channel bandwidth tolerance and signal transmission rate. Under the same data rate, using NLDC can save 5.8 GHz bandwidth for the system. For the bandwidth-limited system, the PS-PAM4 signal can obtain 19Gbit/s bit rate gain compared with the ordinary PAM4 signal. Compared with the typical shaping scheme using CCDM, this scheme can achieve 2.2 GHz band tolerance gain and 5Gbit/s rate gain in nonlinear fiber channel.

A Simple Sign-Bit Probabilistic Shaping Scheme

We propose a new shaping scheme for the Gaussian channel whose complexity is approximately half the one of a binary distribution matcher (DM). The result is obtained as follows: We first show that most of the shaping gain can be obtained via a simplified version of sign-bit shaping, which uses only two non-uniform binary sources. This is achieved by considering a stepwise Maxwell-Boltzmann-like distribution of the symbols. One of the two binary sources has a parameter <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> close to 0. Hence, we then describe a binary DM which explicitly takes advantage of this aspect and has a negligible complexity. Since the two binary sources are used alternately with equal probability, the complexity of the proposed shaping scheme is half the one of the second binary DM.

List-Encoding CCDM: A Nonlinearity-Tolerant Shaper Aided by Energy Dispersion Index

Recently, a metric called energy dispersion index (EDI) was proposed to qualitatively indicate the nonlinear interference (NLI) induced by correlated symbols during optical transmission. In this paper, we propose a new shaper architecture to decrease the EDI of transmitted symbols and thus, increase the signal-to-noise ratio (SNR). We call this shaper the list-encoding constant-composition distribution matcher (L-CCDM). L-CCDM consists of an additional EDI selecting module, which is compatible with standard probabilistic amplitude shaping (PAS) architecture. Numerical results obtained from a multi-span multi-channel system show that when compared to standard CCDM with 256-ary quadrature amplitude modulation (256QAM), the proposed architecture offers an effective SNR gain of 0.35 dB, an achievable information rate gain of 0.22 b/4D-symbol, or equivalently an 8% reach extension.

Experimental Comparison of Orthogonal Frequency Division Multiplexing and Universal Filter Multi-Carrier Transmission

Multi-carrier optical communication schemes are attractive for high-speed mobile fronthaul networks, edge cloud computing and passive optical networks. Compared with conventional orthogonal frequency-division multiplexing (OFDM), universal filter multi-carrier (UFMC) can shape the spectrum of the transmitted signal by introducing universal filter banks. Meanwhile, probabilistic shaping (PS) can make full use of achieved signal-to-noise ratio (SNR) to adaptively adjust the entropy loading according to the measured SNR of each subchannel. However, the significant amount of required distribution matcher (DM) is challenging in the practical implementation. In this work, we experimentally demonstrated 12.5-GBd and 25-GBd PS-UFMC transmissions with approximate 10-GHz bandwidth-limited system over 30-km standard single mode fiber. Due to the sharp cutoff frequency-response of filters, the effect of the frequency decaying in the 25-GBd OFDM system has been eliminated in the UFMC system. Consequently, each subband has similar SNR and therefore the number of required DMs is reduced. Moreover, considering the receiver complexity constraints, the improved bit error ratio performance was achieved by optimizing the allocation of data subbands to mitigate inter symbol interference caused by the dispersion of transmitted fiber.

Probabilistic shaping communication system aided by neural network distribution matcher in data center optical network

AbstractA neural network (NN)‐assisted probabilistic shaping (PS) distribution matcher is proposed, in which the model is simplified by a structured optimization method. The NN algorithm can encode the information sequence, making the signal obey the Gaussian distribution, and can directly restore the received signal. In addition, the algorithm uses the novel training method at both ends of the transmitter and receiver so that the system performance is significantly improved. PS system verification experiments have been carried out under 16QAM‐DMT modulation format. Under the hard decision forward error correction (FEC) threshold of 3.8*10−3 BER, the proposed system achieves 1.1 dB improvement compared to the traditional 16QAM‐DMT system.

Probabilistic Shaping for Protograph LDPC-Coded Modulation by Residual Source Redundancy

Probabilistic amplitude shaping (PAS) has proved to be a promising way to achieve the shaping gain for an additive white Gaussian noise channel with a distribution matcher (DM). However, the DM schemes may suffer a rate loss and increase both complexity and latency, when they are not suited for the input bit stream with redundancy. In this paper, a novel PAS strategy is proposed for a joint source and channel coded modulation system, where the residual source redundancy after source coding can be exploited to obtain both shaping and coding gains. It is shown that the residual source redundancy can be controlled by choosing the row weight distribution for source code, thus making the probability distribution of the modulated symbols be optimized under an appropriate interleaver design. To guarantee the error-floor performance, the source code is constrained by predicting the probability distribution of source bits within target finite-length frames. By jointly designing source and channel codes, the residual source redundancy can also be exploited to achieve the coding gain. Compared with the state-of-the-art code pairs, the proposed code pairs have better error-floor performance, and achieve higher coding and shaping gains without suffering from the rate-loss and the latency caused by DM.

Polar coded probabilistic shaping PAM8 based on many-to-one mapping for short-reach optical interconnection.

In this paper, a polar coded probabilistic shaping (PS) 8-ary pulse amplitude modulation (PAM8) based on many-to-one (MTO) mapping is investigated for short-reach optical interconnection. By ingeniously assigning parity bits to ambiguities positions, no extra PS redundancy and no complex distribution matcher are required in the scheme comparing to traditional probabilistic amplitude shaping (PAS). The noise distributions after different transmission distances are studied and an optimal clock recovery method for PS signal is proposed to degrade the impact of severe eye skew effect on BER performance. The experimental results show that up to 1.2 dB and 0.8 dB shaping gains are respectively achieved over back-to-back (BTB) and 2-km standard single mode fiber (SSMF) transmission. With the help of the proposed optimal clock recovery method in the PS scheme, the shaping gain is improved from 0.15 dB to 0.4 dB after 10-km transmission. Moreover, compared to low-density parity-check (LDPC) code, the polar coded PS-PAM8 can provide an additional coding gain of 2.2 dB with code length of 256, which proves the performance superiority of polar code in short code length. Therefore, the proposed polar coded PS-PAM8 with low complexity and satisfactory BER performance is believed to be an alternative solution for the cost-sensitive short-reach optical interconnection.

Entropy Loading Design for the MIMO-OFDM Visible Light Communication System Using the OCT Precoding Technique

In this paper, an orthogonal circulant matrix transform (OCT) precoding technique is proposed to combine with the entropy loading in the multiple-input multiple-output and orthogonal frequency division multiplexing (MIMO-OFDM) visible light communication (VLC) system where the space-time coding (STBC) is chosen for its robustness to the channel correlation. Benefitting from the OCT precoding technique, the uniform signal-to-noise ratio (SNR) among all the subchannels can be achieved. As a result, only one SNR value is required to be fed back, and the same distribution matcher is employed during probabilistic shaping (PS), which means much lower feedback overhead and system complexity than the conventional entropy loading scheme. Experimental results show that the OCT precoding does not cause the system performance loss where the achievable information rate (AIR) of the proposed system is comparable with the conventional system without precoding. With an available bandwidth of ∼25 MHz, the proposed scheme can realize the AIR of 50.75 Mb/s at the expense of 0.45% average forward error correction (FEC) overhead (OH).

Hierarchical Distribution Matching for Probabilistic Amplitude Shaping.

Probabilistic amplitude shaping—implemented through a distribution matcher (DM)—is an effective approach to enhance the performance and the flexibility of bandwidth-efficient coded modulations. Different DM structures have been proposed in the literature. Typically, both their performance and their complexity increase with the block length. In this work, we present a hierarchical DM (Hi-DM) approach based on the combination of several DMs of different possible types, which provides the good performance of long DMs with the low complexity of several short DMs. The DMs are organized in layers. Each upper-layer DM encodes information on a sequence of lower-layer DMs, which are used as “virtual symbols”. First, we describe the Hi-DM structure, its properties, and the encoding and decoding procedures. Then, we present three particular Hi-DM configurations, providing some practical design guidelines, and investigating their performance in terms of rate loss and energy loss. Finally, we compare the system performance obtained with the proposed Hi-DM structures and with their single-layer counterparts: a SNR gain is obtained by a two-layer Hi-DM based on constant composition DMs (CCDM) compared to a single-layer CCDM with same complexity; a gain and a significant complexity reduction are obtained by a Hi-DM based on minimum-energy lookup tables compared to a single-layer DM based on enumerative sphere shaping with same memory requirements.