The coexistence of QKD and classical communication systems is described, identifying the principal limitations to its practical realization. The relevance of SDN as a suitable approach for a real integration between QKD and WDM networks is presented, together with the description of novel rateless error correcting codes (ECC) suitable for QKD reconciliation. Preliminary experimental results on a discrete-variable QKD field trial, over production optical fibers deployed in the metropolitan area of Turin in presence of high-bitrate classic channels, are reported. Stable performance on a week-long interval is demonstrated, showing the capabilities of QKD in short/medium reach optical networks. This work is part of the activities of the PON project "Development of quantum systems and technologies for IT security in communication networks" (QUANCOM) which aims to the realization of a metropolitan quantum communication network through the collaboration between universities, research centers and companies operating in the communication market area.

Rapporto finale del progetto NeGeFEC2021

Upper bounds on the capacity of vector Gaussian channels affected by fading are derived under peak amplitude constraints at the input. The focus is on constraint regions that can be decomposed in a Cartesian product of sub-regions. This constraint models a transmitter configuration employing a number of power amplifiers less than or equal to the total number of transmitting antennas. In general, the power amplifiers feed distinct subsets of the transmitting antennas and partition the input in independent subspaces. Two upper bounds are derived: The first one is suitable for high signal-to-noise ratio (SNR) values and, as we prove, it is tight in this regime; The second upper bound is accurate at low SNR. Furthermore, the derived upper bounds are applied to the relevant case of amplitude constraints induced by employing a distinct power amplifier for each transmitting antenna.

This letter introduces an analytical model that gives the expected asymptotic cumulative number of molecules absorbed by each spherical receiver in a diffusive multiple-input multiple-output (MIMO) molecular communication (MC) system with pointwise transmitters. The reciprocal effect among the fully absorbing (FA) receivers is taken into account by using the recently introduced concept of fictitious pointwise negative source of molecules. An agreement is shown between the proposed asymptotic model and the numerical solution of the exact analytical one from the literature describing the interaction among the receivers, which is computed for a sufficient long time.

In this paper an analytical model is introduced to describe the impulse response of the diffusive channel between a pointwise transmitter and a given fully-absorbing (FA) receiver in a molecular communication (MC) system. The presence of neighbouring FA nanomachines in the environment is taken into account by describing them as sources of negative molecules. The channel impulse responses of all the receivers are linked in a system of integral equations. The solution of the system with two receivers is obtained analytically. For a higher number of receivers the system of integral equations is solved numerically. It is also shown that the channel impulse response shape is distorted by the presence of the neighbouring FA interferers. For instance, there is a time shift of the peak in the number of absorbed molecules compared to the case without interference, as predicted by the proposed model. The analytical derivations are validated by means of particle based simulations.

Rapporto finale del progetto NeGeFEC20

An upper bound on the capacity of multiple-input multiple-output (MIMO) additive white Gaussian noise fading channels is derived under peak amplitude constraints. The tightness of the bound is investigated at high signal-to-noise ratio (SNR), for any arbitrary convex amplitude constraint region. Moreover, a numerical simulation of the bound for fading MIMO channels is analyzed, at any SNR level, for a practical transmitter configuration employing a single power amplifier for all transmitting antennas.

The capacity of multiple-input multiple-output additive white Gaussian noise channels is investigated under peak amplitude constraints on the norm of the input vector. New insights on the capacity-achieving input distribution are presented. Furthermore, it is provided an iterative algorithm to numerically evaluate both the information capacity and the optimal input distribution of such channel.

We report experimental results on a QKD field trial over production optical fibers deployed in the metropolitan area of Turin in presence of high-bitrate classic channels. Stable performance on a week-long interval is demonstrated.

In this paper, we consider spatially coupled LDPC codes derived from protographs. In particular, we analyze the performance of the window decoder (WD), which allows reducing the complexity, the memory requirements, and the latency of the flood belief-propagation decoder. We show that the performance degradation of WD is due to the fact that it exploits a single decoding wave instead of two. This has effect both in the ideal case of infinite code length, where it may imply a threshold loss, and in the case of finite length, where it affects the slope of the BER curve in the waterfall region. We show how a forward-backward decoder can reduce such problems at the price of a limited increase of average complexity.

The design of molecular communication systems over a diffusive channel has been extensively studied under the hypothesis of a point-wise transmitter and one receiving cell that absorbs molecules from the environment. Recent works have extended this scenario by including also the effect of one, or more, interfering cells that introduce a perturbation in the number of molecules absorbed by the target receiving cell. In this paper we exploit such a perturbation to estimate the relative angle under which the receiver sees the interferer with respect to the transmitter. The mean-squared error of the relative angle estimation is reported for different distances between interferer and receiver. As a main result, we show that the interfering cell introduces two effects, namely "blocking" and "shadowing", that strongly affect the angle assessment. Simulation results are supported by the derivation of an analytical model that is able to make a good prediction of the average number of molecules absorbed by the target receiver as a function of the position of the interferer. Our numerical results show that, for the selected hypotheses, the best performance for the angle estimation is achieved when it is around 30o.

We evaluate capacity bounds for multiple-input multiple-output (MIMO) additive white Gaussian noise (AWGN) fading channels subject to input amplitude constraints. We focus on two practical cases, in which the transmitter: (i) employs a single antenna amplifier, which induces a constraint on the norm of the input vector, and (ii) it employs multiple amplifiers, one per antenna, which leads to independent constraints on the amplitude of each input vector entry. For both cases, we evaluate the asymptotic capacity gap between upper and lower bounds at high signal-to-noise ratio.

Absorbing sets (ASs) cause the error floor phenomenon in many low-density parity-check (LDPC) codes by entrapping iterative decoders. A recent simplified system model for practical min-sum (MS) LDPC decoding predicts that if all variable nodes in an AS have channel messages above a certain threshold, the AS cannot entrap the decoder. The threshold is an AS parameter that depends on its Tanner graph, and is the result of a nonlinear optimization. In this paper, we analyze the messages exchanged in the directed graph (digraph) of the AS during MS decoding while evaluating the AS threshold. By doing this, we unveil the meaning of the threshold value, which is the minimum channel message for which positive feedback loops in the digraph involve all the messages exchanged.

Rapporto finale dell'omonimo contratto di ricerca.

Final report of the project Next Generation FEC and Constellation shaping (2018) for coherent optical communications.

In this paper, the definition of threshold of elementary absorbing sets is extended to scaled Min-Sum lowdensity parity-check (LDPC) decoding. Based on the analysis of the behavior of scaled Min-Sum LDPC decoders in the Tanner graph of the absorbing set, it is proven that correct decoding is guaranteed with received channel messages above threshold. A fast algorithm for the threshold computation is derived. Many examples of absorbing sets taken from LDPC codes of various variable node degrees are investigated, and it is shown that all of them can be deactivated with low enough scaling factors.

Emerging memory technologies (like PCM, MRAM and 3D XPoint) can make data storage as fast as the rest of the system. But to cope with the reliability targets of storage applications, error correcting codes (ECCs) able to correct many errors might be needed anyway. Hierarchical codes, ECCs enabling two levels of correction, can be good candidates to satisfy these reliability targets, without impacting (on average) the low-latency characteristics of these technologies. In particular, an Ultra-Fast (UF) ECC can be used as first trial as long as it is able to flag its failures with high probability and low latency. In this paper we design an UF-ECC able to produce a check for incorrect decoding with probability lower than the typical target uncorrectable bit-error rate (UBER) of storage applications (e.g. 1e-15) and with a latency comparable with the UF-ECC correction process.

In this paper we propose a definition of Absorbing Sets for binary Generalized LDPC (GLDPC) codes. We show that under practical Max-Log iterative decoding, our AS definition enables a local description of the message evolution with the iterations, with a simplified model very similar to the one used for the analysis of Min-Sum LDPC decoding. Accordingly, these ASs exhibit a threshold behavior also in GLDPC codes.

Shaping of multilevel constellations is investigated and it is shown that the performance in the waterfall region can be accurately predicted on the basis of the performance of the LDPC codes on the Binary AWGN channel. The use of punctured LDPC codes, not investigated so far in combination with shaped constellations, is checked to verify if it offers some additional gain. Some final work on the LDPC code implementation is still needed, to simplify the encoder and to reduce the power consumption of the decoder.

Abstract--Absorbing sets (ASs) cause the error floor phenomenon in many Low-Density Parity-Check (LDPC) codes. A recent, simplified system model for Min-Sum (MS) LDPC decoding [1] predicts that ASs exhibit a threshold behavior: if all variable nodes in an AS have channel messages above the threshold, the AS cannot trap the decoder. The threshold is a real-valued parameter that depends on the topology of the AS, and can be evaluated by a nonlinear optimization. In this paper we describe a simple, fast algorithm for evaluating the AS threshold. Additionally, we show that the algorithm is valid also for scaled-MS decoding. We show with an example that the threshold values under scaled-MS decoding are smaller than underMS decoding. Accordingly, scaling decreases the error floor.