Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

In this paper, we provide for the first time a systematic comparison of distribution matching (DM) and sphere shaping (SpSh) algorithms for short blocklength probabilistic amplitude shaping. For asymptotically large blocklengths, constant composition distribution matching (CCDM) is known to generate the target capacity-achieving distribution. As the blocklength decreases, however, the resulting rate loss diminishes the efficiency of CCDM. We claim that for such short blocklengths and over the additive white Gaussian channel (AWGN), the objective of shaping should be reformulated as obtaining the most energy-efficient signal space for a given rate (rather than matching distributions). In light of this interpretation, multiset-partition DM (MPDM), enumerative sphere shaping (ESS) and shell mapping (SM), are reviewed as energy-efficient shaping techniques. Numerical results show that MPDM and SpSh have smaller rate losses than CCDM. SpSh--whose sole objective is to maximize the energy efficiency--is shown to have the minimum rate loss amongst all. We provide simulation results of the end-to-end decoding performance showing that up to 1 dB improvement in power efficiency over uniform signaling can be obtained with MPDM and SpSh at blocklengths around 200. Finally, we present a discussion on the complexity of these algorithms from the perspective of latency, storage and computations.Comment: 18 pages, 10 figure

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

Voronoi Constellations for Coherent Fiber-Optic Communication Systems

The increasing demand for higher data rates is driving the adoption of high-spectral-efficiency (SE) transmission in communication systems. The well-known 1.53 dB gap between Shannon\u27s capacity and the mutual information (MI) of uniform quadrature amplitude modulation (QAM) formats indicates the importance of power efficiency, particularly in high-SE transmission scenarios, such as fiber-optic communication systems and wireless backhaul links. Shaping techniques are the only way to close this gap, by adapting the uniform input distribution to the capacity-achieving distribution. The two categories of shaping are probabilistic shaping (PS) and geometric shaping (GS). Various methods have been proposed for performing PS and GS, each with distinct implementation complexity and performance characteristics. In general, the complexity of these methods grows dramatically with the SE and number of dimensions.Among different methods, multidimensional Voronoi constellations (VCs) provide a good trade-off between high shaping gains and low-complexity encoding/decoding algorithms due to their nice geometric structures. However, VCs with high shaping gains are usually very large and the huge cardinality makes system analysis and design cumbersome, which motives this thesis.In this thesis, we develop a set of methods to make VCs applicable to communication systems with a low complexity. The encoding and decoding, labeling, and coded modulation schemes of VCs are investigated. Various system performance metrics including uncoded/coded bit error rate, MI, and generalized mutual information (GMI) are studied and compared with QAM formats for both the additive white Gaussian noise channel and nonlinear fiber channels. We show that the proposed methods preserve high shaping gains of VCs, enabling significant improvements on system performance for high-SE transmission in both the additive white Gaussian noise channel and nonlinear fiber channel. In addition, we propose general algorithms for estimating the MI and GMI, and approximating the log-likelihood ratios in soft-decision forward error correction codes for very large constellations

Performance Prediction of Nonbinary Forward Error Correction in Optical Transmission Experiments

In this paper, we compare different metrics to predict the error rate of optical systems based on nonbinary forward error correction (FEC). It is shown that the correct metric to predict the performance of coded modulation based on nonbinary FEC is the mutual information. The accuracy of the prediction is verified in a detailed example with multiple constellation formats, FEC overheads in both simulations and optical transmission experiments over a recirculating loop. It is shown that the employed FEC codes must be universal if performance prediction based on thresholds is used. A tutorial introduction into the computation of the threshold from optical transmission measurements is also given.Comment: submitted to IEEE/OSA Journal of Lightwave Technolog

Constellation design for future communication systems: a comprehensive survey

[EN] The choice of modulation schemes is a fundamental building block of wireless communication systems. As a key component of physical layer design, they critically impact the expected communication capacity and wireless signal robustness. Their design is also critical for the successful roll-out of wireless standards that require a compromise between performance, efficiency, latency, and hardware requirements. This paper presents a survey of constellation design strategies and associated outcomes for wireless communication systems. The survey discusses their performance and complexity to address the need for some desirable properties, including consistency, channel capacity, system performance, required demapping architecture, flexibility, and independence. Existing approaches for constellation designs are investigated using appropriate metrics and categorized based on their theoretical algorithm design. Next, their application to different communication standards is analyzed in context, aiming at distilling general guidelines applicable to the wireless building block design. Finally, the survey provides a discussion on design directions for future communication system standardization processes.This work was supported in part by the Basque Government under Grant IT1234-19, in part by the PREDOC under Program PRE_2020_2_0105, and in part by the Spanish Government through the Project PHANTOM (MCIU/AEI/FEDER, UE) under Gran

Spectral Efficient Coding Schemes in Optical Communications

Abstract Achieving high spectral efficiency in optical transmissions has recently attracted much attention, aiming to satisfy the ever increasing demand for high data rates in optical fiber co mmun ications. Therefore, strong Forward Error Correct ion (FEC) coding in co mb ination with mult ilevel modulat ion schemes is mandatory to approach the channel capacity of the transmission link. In this paper we g ive design rules on the joint optimization of coding and signal constellations under practical considerations. We give trade-offs between spectral efficiency and hardware complexity, by comparing coding schemes using capacity achieving constellations with bit-interleaved coded modulation and iterative decoding (BICM-ID) against applying conventional square quadrature amp litude modulation (QAM) constellations but emp loying powerful low co mplexity lo w-density parity-check (LDPC) codes. Both schemes are suitable for optical single carrier (SC) and optical orthogonal frequency-division mu ltiplexing (OFDM) transmission systems, where we consider the latter one in this paper, due to well-studied equalizat ion techniques in wireless communications. We numerically study the performance of different coded modulation formats in optical OFDM transmission, showing that for a fiber optical transmission lin k of 960 km reach the net spectral efficiency can be increased by ≈0.4 bit/s/Hz to 8.61 b it/s/Hz at a post FEC BER of <10 -15 by using coded optimized constellations instead of coded 64-QAM