Post-FEC BER Benchmarking for Bit-Interleaved Coded Modulation with Probabilistic Shaping

Accurate performance benchmarking after forward error correction (FEC) decoding is essential for system design in optical fiber communications. Generalized mutual information (GMI) has been shown to be successful at benchmarking the bit-error rate (BER) after FEC decoding (post-FEC BER) for systems with soft-decision (SD) FEC without probabilistic shaping (PS). However, GMI is not relevant to benchmark post-FEC BER for systems with SD-FEC and PS. For such systems, normalized GMI (NGMI), asymmetric information (ASI), and achievable FEC rate have been proposed instead. They are good at benchmarking post-FEC BER or to give an FEC limit in bit-interleaved coded modulation (BICM) with PS, but their relation has not been clearly explained so far. In this paper, we define generalized L-values under mismatched decoding, which are connected to the GMI and ASI. We then show that NGMI, ASI, and achievable FEC rate are theoretically equal under matched decoding but not under mismatched decoding. We also examine BER before FEC decoding (pre-FEC BER) and ASI over Gaussian and nonlinear fiber-optic channels with approximately matched decoding. ASI always shows better correlation with post-FEC BER than pre-FEC BER for BICM with PS. On the other hand, post-FEC BER can differ at a given ASI when we change the bit mapping, which describes how each bit in a codeword is assigned to a bit tributary.Comment: 14 pages, 8 figure

Analysis of hybrid-ARQ based relaying protocols under modulation constraints

In a seminal paper published in 2001, Caire and Tuninetti derived an information theoretic bound on the throughput of hybrid-ARQ in the presence of block fading. However, the results placed no constraints on the modulation used, and therefore the input to the channel was Gaussian. The purpose of this thesis is to investigate the impact of modulation constraints on the throughput of hybrid-ARQ in a block fading environment. First, we consider the impact of modulation constraints on information outage probability for a block fading channel with a fixed length codeword. Then, we consider the effect of modulation constraints upon the throughput of hybrid-ARQ, where the rate of the codeword varies depending on the instantaneous channel conditions. These theoretical bounds are compared against the simulated performance of HSDPA, a newly standardized hybrid-ARQ protocol that uses QPSK and 16-QAM bit interleaved turbo-coded modulation. The results indicate how much of the difference between HSDPA and the previous unconstrained modulation bound is due to the use of the turbo-code and how much is due to the modulation constraints. (Abstract shortened by UMI.)

Polarization-ring-switching for nonlinearity-tolerant geometrically-shaped four-dimensional formats maximizing generalized mutual information

In this paper, a new four-dimensional 64-ary polarization ring switching (4D-64PRS) modulation format with a spectral efficiency of 6 bit/4D-sym is introduced. The format is designed by maximizing the generalized mutual information (GMI) and by imposing a constant-modulus on the 4D structure. The proposed format yields an improved performance with respect to state-of-the-art geometrically shaped modulation formats for bit-interleaved coded modulation systems at the same spectral efficiency. Unlike previously published results, the coordinates of the constellation points and the binary labeling of the constellation are jointly optimized. When compared with polarization-multiplexed 8-ary quadrature-amplitude modulation (PM-8QAM), gains of up to 0.7 dB in signal-to-noise ratio are observed in the additive white Gaussian noise (AWGN) channel. For a long-haul nonlinear optical fiber system of 8,000 km, gains of up to 0.27 bit/4D-sym (5.5% data capacity increase) are observed. These gains translate into a reach increase of approximately 16% (1,100 km). The proposed modulation format is also shown to be more tolerant to nonlinearities than PM-8QAM. Results with LDPC codes are also presented, which confirm the gains predicted by the GMI.Comment: 12 pages, 12 figure

Machine Learning in Digital Signal Processing for Optical Transmission Systems

The future demand for digital information will exceed the capabilities of current optical communication systems, which are approaching their limits due to component and fiber intrinsic non-linear effects. Machine learning methods are promising to find new ways of leverage the available resources and to explore new solutions. Although, some of the machine learning methods such as adaptive non-linear filtering and probabilistic modeling are not novel in the field of telecommunication, enhanced powerful architecture designs together with increasing computing power make it possible to tackle more complex problems today. The methods presented in this work apply machine learning on optical communication systems with two main contributions. First, an unsupervised learning algorithm with embedded additive white Gaussian noise (AWGN) channel and appropriate power constraint is trained end-to-end, learning a geometric constellation shape for lowest bit-error rates over amplified and unamplified links. Second, supervised machine learning methods, especially deep neural networks with and without internal cyclical connections, are investigated to combat linear and non-linear inter-symbol interference (ISI) as well as colored noise effects introduced by the components and the fiber. On high-bandwidth coherent optical transmission setups their performances and complexities are experimentally evaluated and benchmarked against conventional digital signal processing (DSP) approaches. This thesis shows how machine learning can be applied to optical communication systems. In particular, it is demonstrated that machine learning is a viable designing and DSP tool to increase the capabilities of optical communication systems

Efficient simulation of communication systems on a desktop grid

Simulation is an important part of the design cycle of modern communication systems. As communication systems grow more sophisticated, the computational burden of these simulations can become excessive. The need to rapidly bring systems to market generally precludes the use of a single computer, and drives a demand for parallel computation. While this demand could be satisfied by the development of dedicated infrastructure, a more efficient option is to harness the unused computational cycles of underutilized desktop computers located throughout the organization.;In this thesis, a new paradigm for parallelizing communication simulations is proposed and developed. A desktop grid is created by running a compute engine as a background job on existing computers located throughout the University. The compute engine takes advantage of unused cycles to run simulations, and reports its results back to a server. The simulation itself is developed and launched from a client machine using Matlab, an application that has widespread acceptance within the communications industry. To obviate the need for a Matlab license on every machine running the compute engine, the simulation is first compiled to stand-alone executable code, and the executable and input data files are distributed to the grid machines over the Internet. To illustrate the performance improvement, a campaign of 16 distinct simulations corresponding to the IEEE 802.11a standard is run over the grid. Each compute engine executes a single simulation corresponding to one of eight modulation and coding schemes and one of two channel models. The improvement in execution time is quantified by a tool that was developed to monitor the activity of the grid

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

Quantum key security : theory and analysis of experimental realisations

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Constellation Shaping for Bit-Interleaved LDPC Coded APSK

An energy-efficient approach is presented for shaping a bit-interleaved low-density parity-check (LDPC) coded amplitude phase-shift keying (APSK) system. A subset of the interleaved bits output by a binary LDPC encoder are passed through a nonlinear shaping encoder whose output is more likely to be a zero than a one. The "shaping" bits are used to select from among a plurality of subconstellations, while the unshaped bits are used to select the symbol within the subconstellation. Because the shaping bits are biased, symbols from lower-energy subconstellations are selected more frequently than those from higher-energy subconstellations. An iterative decoder shares information among the LDPC decoder, APSK demapper, and shaping decoder. Information rates are computed for a discrete set of APSK ring radii and shaping bit probabilities, and the optimal combination of these parameters is identified for the additive white Gaussian noise (AWGN) channel. With the assistance of extrinsic-information transfer (EXIT) charts, the degree distributions of the LDPC code are optimized for use with the shaped APSK constellation. Simulation results show that the combination of shaping, degree-distribution optimization, and iterative decoding can achieve a gain in excess of 1 dB in AWGN at a rate of 3 bits/symbol compared with a system that does not use shaping, uses an unoptimized code from the DVB-S2 standard, and does not iterate between decoder and demodulator.Comment: to appear in IEEE Transactions on Communication