Soft-metric based channel decoding for photon counting receivers
Marina Mondin, Fred Daneshgaran, Inam Bari, Maria Teresa Delgado, Stefano Olivares, Matteo G. A. Paris
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Soft-metric based channel decoding for photoncounting receivers
Marina Mondin, Fred Daneshgaran, Inam Bari, Maria Teresa Delgado,Stefano Olivares, and Matteo G. A. Paris
Abstract —We address photon-number-assisted, polarization-based, binary communication systems equipped with photoncounting receivers. In these channels information is encoded inthe value of polarization phase-shift but the carrier has andadditional degree of freedom, i.e. its photon distribution, whichmay be exploited to implement binary input-multiple output(BIMO) channels also in the presence of a phase-diffusion noiseaffecting the polarization. Here we analyze the performances ofthese channels, which approach capacity by means of iterativelydecoded error correcting codes. In this paper we use soft-metric-based low density parity check (LDPC) codes for this purpose.In order to take full advantage of all the information availableat the output of a photon counting receiver, soft information isgenerated in the form of log-likelihood ratios, leading to improvedframe error rate (FER) and bit error rate (BER) comparedto binary symmetric channels (BSC). We evaluate the classicalcapacity of the considered BIMO channel and show the potentialgains that may be provided by photon counting detectors inrealistic implementations.
Index Terms —Quantum communication, photon detectors
I. I
NTRODUCTION I N binary optical communication, the logical informationis encoded onto two different states of the radiation field.After the propagation, the receiver should perform a mea-surement, aimed at discriminating the two signals. Currently,most of the long-distance amplification-free optical classicalcommunication schemes employ relatively weak laser sourcesleading to small mean photon count values at the receiver.The same is true for quantum-enhanced secure cryptographicprotocols. In fact, laser radiation, which is described by co-herent states, preserves its Poissonian photon-number statisticsand polarization also in the presence of losses. On the otherhand, operating in the regime of low number of detectedphotons gives rise to the problem of discriminating the signalsby quantum-limited measurements [1], [2], [3]. Indeed, thebinary discrimination problem for coherent states has beenthoroughly investigated, both for its fundamental interest and
M. Mondin is with the Dipartimento di Elettronica e Telecomunicazioni,Politecnico di Torino, 10129 Torino, Italy, e-mail: [email protected]. Daneshgaran is with the Electrical and Computer Eng. Dept., CaliforniaState Univ., Los Angeles, CA, USA, e-mail: [email protected]. Bari is with the National University of Computer and Emerging Sciences(FAST-NU), Peshawar, Pakistan e-mail: [email protected]. T. Delgado is with the Dipartimento di Elettronica e Tele-comunicazioni, Politecnico di Torino, 10129 Torino, Italy, e-mail:[email protected]. Olivares is with the Dipartimento di Fisica, Universit`a degli Studi diMilano, I-20133 Milano, Italy, e-mail: stafano.olivares@fisica.unimi.itM. G. A. Paris is with the Dipartimento di Fisica, Universit`a degli Studidi Milano, I-20133 Milano, Italy, e-mail: matteo.paris@fisica.unimi.it for practical purposes [4], [5], [6], [7], [8], [9]. It shouldbe mentioned however that in order to exploit the phaseproperties of coherent states, one should implement phasesensitive receivers [10], [11] with nearly optimal performancesalso in the presence of dissipation and noise [7], [12]. This is achallenging task, since it is generally difficult, and sometimesimpossible, to have a suitable and reliable phase reference inorder to implement this kind of receiver [13].The simplest choice for a detection scheme involving radi-ation is given by detectors which simply reveal the presenceor the absence of radiation (on/off detectors) with acceptabledead-time values and dark count rates. A natural evolution ofsuch schemes would be to employ photon counting receivers.Indeed, development of photon counters has been extensivelypursued in the last decades, as well as of methods to extractthe photon distribution by other schemes [14], [15], [16],[17], [18]. Given that one could use photon counting detectorsfor weak-energy optical communications, a question arises onwhether and how such detectors may be employed to improvethe system performance. A possible way to answer this ques-tion is to determine the capacity of the corresponding opticalchannels, and the achievable residual Bit Error Rate (BER) andFrame Error Rate (FER) of practical communication schemesover these channels. A photon counting detector is clearlyable to extract more information than a simple on/off detector.The practical consequence is that a photon counting detectorallows one to generate a meaningful log-likelihood (i.e. a soft-metric), as opposed to a hard-metric allowed by a hard- (oron/off) detector. Furthermore, soft-metrics lead to improvedperformances when exploited by powerful iteratively decodedforward error correcting codes.Recently, a simple polarization-based communicationscheme involving weak coherent optical signals and low-complexity photon counting receivers has been presented [1],and its performances have been analyzed based on an equiv-alent Binary Symmetric Channel (BSC) model of the overallscheme. In this paper, we extend the scheme of [1] and modelthe effect of the photon distribution of the coherent signals asa time varying Binary Input-Multiple Output (BIMO) channel.In particular, we employ soft-metric based Low Density ParityCheck (LDPC) codes for transmission over the BIMO channelto approach capacity using iteratively decoded error correctingcodes and investigate the potential improvements that may beobtained in terms of classical capacity and residual BER usingphoton counting receivers [27]. It is worth noting that recentlyphoton-counting detectors have been proposed to enhancethe discrimination of weak optical signal in the case of M - a r X i v : . [ qu a n t - ph ] D ec OURNAL OF L A TEX CLASS FILES 2 ary coherent state discrimination [28], [29]: in these cases,however, a suitable feedback scheme or the use of squeezingare required.The receiver introduced in [1] is based on an optical setupfor one-parameter qubit gate optimal estimation [2], [21], [19].In this scheme, the qubit is encoded in the polarization degreeof freedom of a light beam, whose intensity (photon) degreeof freedom has been prepared in a coherent state, and the one-parameter gate corresponds to a polarization transformation. Inthe ideal case, orthogonal polarization states can be perfectlydiscriminated. However, in a realistic scenario and especiallyin free-space communication, non-dissipative (diffusive) noiseaffecting light polarization disturbs the orthogonality of thestates at the receiver, thus requiring suitable detection andstrategy for discrimination. It is worth noting that coherentstates preserve their fundamental properties when propagatingin purely lossy channels, suffering only attenuation, thus onlythe noise affecting the polarization is detrimental. Remarkably,since our receiver is phase-insensitive, the scheme works aswell as when phase-diffusion noise is affecting the channel.This also holds in the case of phase-randomized coherentstates [22] which can be easily generated, characterized andmanipulated [23] and are useful for enhancing security indecoy state quantum key distribution [24], [25].The paper is organized as follows; the physical systemis described in Section II, where the corresponding channelmodel and log-likelihood metric are also defined. The as-sociated channel capacity is evaluated in Section IV, whilethe achievable residual frame and bit error rate obtained withLDPC coding is presented in Section V. Section VI concludesthe paper with some final remarks.II. T
HE PHYSICAL CHANNEL
The channel we are going to investigate corresponds to theoptical setup schematically depicted in Fig. 1. The informationbit is encoded onto the polarization degree of freedom of alight beam prepared in a coherent state | α (cid:105) , initially linearlypolarized at ◦ with respect to the x -axis, i.e.: | α (cid:105) ⊗ | + (cid:105) = | α (cid:105) ⊗ (cid:18) | H (cid:105) + | V (cid:105)√ (cid:19) , where | H (cid:105) and | V (cid:105) denote horizontal and vertical polarizationstates with respect to the x -axis. The encoding rule for the bit k = 0 , is applied to the qubit by means of the polarizationrotation U ( φ k ) = e − i φ k σ , σ being the Pauli matrix. Dueto the analogy with the phase-shift encoding, from now onwe will refer to U ( φ k ) as “phase shift”. In order to followthe scheme proposed in Refs. [1] and in view of a possibleexperimental verification reported in [21], [19], we assumethat the encoding rule for the bit given in Table I. k −→ φ k −→ π/ −→ π/ Table IE
NCODING RULE FOR THE POLARIZATION PHASE - SHIFT . Figure 1. Schematic diagram of the optical setup implementing photon-number-assisted, polarization-based, binary communication channels equippedwith photon counting receivers.
The polarization rotation (phase shift) may be easily imple-mented by means of a KDP crystal driven by a high voltagegenerator, and corresponds to a change of the polarizationfrom linear to elliptical. At the detection stage informationis retrieved by intensity measurement, in a scheme involvinga Half-Wave Plate (HWP), a Polarizing Beam Splitter (PBS)and two photon counters. This scheme has been experimentallytested to achieve one-parameter qubit gate optimal estimation[21], [19]. Furthermore, several examples of detectors nowused by the quantum optics community, can be used as photoncounters [15], [16], [17], [21], [22], [23]. The outcomes of themeasurement are thus pairs of integer numbers ( n , n ) , where n k is the number of detected photons in the reflected ( k = 0) and transmitted ( k = 1) beam, respectively. Notice that thetotal number of detected photons n = n + n is varying shotby shot. We assume that no photon is lost at the beam splitter.The number of photons in the coherent carrier is a Poissondistributed random variable with mean value N c = | α | . Alsothe two beams after the PBS are coherent states and the jointprobability of obtaining the outcome ( n , n ) is the product oftwo factorized Poisson distributions. The mean values dependon the polarization phase-shift, i.e. on the bit value. Upondenoting by N k ( φ ) the mean photon number in the reflectedor transmitted beam when the imposed phase-shift is φ , wehave: N ( φ ) = 12 N c (1 + cos φ ) , N ( φ ) = 12 N c (1 − cos φ ) . The probability of the event ( n , n ) is thus given by: p ( n , n | φ ) = e − N ( φ ) − N ( φ ) N ( φ ) n n ! N ( φ ) n n != e − N c N ( φ ) n n ! N ( φ ) n n ! . (1)The overall scheme is suitable for working with weak opticalsignals, where the value of N c is typically small. The relevantobservation to be made here is that the information is retrievedby photon counting, and therefore the discrete bit value k ,encoded in the polarization qubit, is mapped at the detectionstage onto pairs of integer numbers. The considered schemecan be modeled as shown in Fig. 2, i.e. with an equivalentbinary-input/multiple-output channel that receives the binaryrandom variable k as input, and generates the two randomvariables n , n as outputs. In particular, for a given number n of detected photons, there are n + 1 pairs n , n such that n + n = n . The availability of multiple outputs, whose OURNAL OF L A TEX CLASS FILES 3 likelihood can be exploited for soft-information processing, isa crucial characteristic of the described scheme.
Figure 2. BIMO channel model of the considered system.
If propagation of the light beam occurs in an environment,which perturbs the polarization but preserves the energy, thenthe state impinging onto the PBS has no longer a well-definedpolarization (phase): If the initial state is | φ k (cid:105) ⊗ | α (cid:105) , where | φ k (cid:105) = U ( φ k ) | + (cid:105) refers to the polarization qubit, the phase-diffusion noise affects the polarization according to the map[21]: | φ k (cid:105) → (cid:37) k = (cid:90) R dϕ g ( ϕ, ∆) U ( ϕ ) | φ k (cid:105) (cid:104) φ k | U † ( ϕ ) , (2)where (cid:37) k represents the density matrix of the degraded po-larization qubit and g ( ϕ, ∆) is a normal distribution of thevariable ϕ with zero mean and standard deviation ∆ . Fromthe physical point of view, Eq. (2) follows from a Masterequation approach [30] which represents a dynamics in whichthe quantum state of light undergoes an energy conservingscattering affecting the polarization. Overall, this correspondsto applying a random polarization rotation (or phase shift)of the input polarization distributed according to g ( ϕ, ∆) .The probabilities of the outcomes are still given by Eq. (1),however with the mean photon numbers modified to: N ( φ, ∆) ≡ N ( φ ) = 12 N c (1 + e − ∆ cos φ ) , (3) N ( φ, ∆) ≡ N ( φ ) = 12 N c (1 − e − ∆ cos φ ) . (4)III. E VALUATION OF THE L OG -L IKELIHOOD R ATIOS
Soft-decoding algorithms are typically based on the useof Log-Likelihood-Ratios (LLR). In our particular case, theLLR values associated to the channel model of Fig. 2 can beevaluated as:LLR ( n , n ) = log (cid:20) p ( φ | n , n ) p ( φ | n , n ) (cid:21) (5)where, p ( φ k |{ n , n } ) k = 0 , (6)is the probability that the transmitted bit was “ k ” given theoutcomes ( n , n ) . Using Bayes theorem, Eq. (5) may berewritten as:LLR ( n , n ) = log (cid:20) p ( n , n | φ ) p ( n , n | φ ) (cid:21) . (7)Finally, using Eq. (1) we arrive at:LLR ( n , n ) = ( n − n ) log (cid:18) q − q (cid:19) (8) where, q = 12 (cid:104) − e − ∆ cos (cid:16) π (cid:17)(cid:105) , (9)for the chosen encoding. The system described up to this pointrepresents, for a given n , a BIMO Discrete Memoryless Chan-nel (DMC) [20] with binary input k and n + 1 = n + n + 1 outputs ( n , n ) , where n is a Poisson distributed randomvariable. In the next Section we will evaluate the capacityof this channel.IV. E VALUATION OF CAPACITY
A sufficient statistic for detection with photon countingdetectors is the difference photocurrent at the output, i.e. D = n − n . Since the two random variables n and n arePoisson distributed, the outcome d of D is Skellam distributed,namely: p D ( d | φ ) = e − N c (cid:20) N ( φ ) N ( φ ) (cid:21) d/ I | d | (cid:16) (cid:112) N ( φ ) N ( φ ) (cid:17) , (10)where I m ( z ) is the modified Bessel function of the first kind,such that: p D ( d | φ k ) = e − N c (cid:18) q − q (cid:19) ( − k d/ I | d | (cid:16) N c (cid:112) q (1 − q ) (cid:17) . (11)Upon denoting by Φ the input binary variable, the relevantfigure of merit to evaluate the channel capacity is the mutualinformation: I (Φ , D ) = H (Φ) − H (Φ | D ) , where, H (Φ) = − z log z − z log z , is the Shannon entropy of the input alphabet, z ( z = 1 − z )being the a-priori probability of sending the bit k = 0 ( k = 1 )and H (Φ | D ) is the conditional entropy: H (Φ | D ) = − (cid:88) k,d p D ( d ) p ( φ k | d ) log p ( φ k | d ) and, p D ( d ) = z p D ( d | φ ) + (1 − z ) p D ( d | φ ) (12)is the overall probability of the outcome d , irrespective of theinput bit.Our BIMO DMC is neither symmetric nor weakly sym-metric. Recall that a DMC is said to be symmetric if therows (and the columns) of the channel transition probabilitymatrix are permutations of each other. If, on the other hand, therows are permutations of each other and the column sums areequal but the columns are not permutations of each other, theDMC is said to be weakly symmetric. It can be shown that forsymmetric or weakly symmetric channels uniform probabilityon input maximizes the mutual information thus yieldingcapacity. However, it can be easily shown that the inputprobability distribution maximizing the mutual information in OURNAL OF L A TEX CLASS FILES 4 the BIMO case above is the uniform one, i.e. z = z = 1 / .The channel capacity is thus given by: C = max z I (Φ | D )= 1 + 12 (cid:88) k,d [ p D ( d | φ ) + p D ( d | φ )] p ( φ k | d ) log p ( φ k | d ) . (13)Our goal is now to compare the capacity of the presentphoton counting receiver channel to that of the equivalentbinary symmetric channel resulting from the detection ofoptical signals by on/off receiver, which just discriminatesthe presence or the absence of radiation (i.e., performs harddecoding). The transition probability of the equivalent BSCassociated with the considered photon counting receiver (i.e.the raw BER, denoted in the following as QBER) can beobtained as:QBER = ∞ (cid:88) m =1 p D ( m | φ ) + 12 p D (0 | φ ) , (14) = ∞ (cid:88) m =1 p D ( − m | φ ) + 12 p D (0 | φ ) . (15)Essentially, assuming φ is true, a detection error occurs for ahard decision detector if D = n − n > . In case D = 0 , thedetector can toss a fair coin and assign a decoded bit arbitrarily,in which case the probability of error is p D (0 | φ ) .In our case, in the limit N c (cid:29) , we can write: N ( φ k ) N ( φ k ) = p (1 | φ k ) p (0 | φ k ) and, N ( φ k ) N ( φ k ) = N c p (1 | φ k ) p (0 | φ k ) . When “ is transmitted and it is mapped to φ ”, we get fromEqs. (3) and (4): p D ( m | φ ) = e − N c (cid:112) α m ∆ B m ( N c , ∆); analogously when “1 is transmitted and it is mapped to φ ” : p D ( m | φ ) = e − N c (cid:112) α m ∆ B m ( N c , ∆) , where, α ∆ = √ e − ∆ √ − e − ∆ , and, B m ( N c , ∆) = I | m | (cid:32) N c (cid:114) − e − (cid:33) . After some manipulation we have: p ,m ≡ p ( φ | D = m ) = z z (1 − α m ∆ ) + α m ∆ ,p ,m ≡ p ( φ | D = m ) = 1 − z z (1 − α m ∆ ) + α m ∆ . The final expression of the conditional entropy as a functionof the two parameters N c and ∆ is: H (Φ | D ) = − e − N c (cid:88) m z B m ( N c , ∆) (cid:112) α m ∆ log ( p ,m ) − e − N c (cid:88) m (1 − z ) B m ( N c , ∆) (cid:112) α m ∆ log ( p ,m ) . Note that capacity is achieved with z = . The results areshown in Fig. 3 and 4. The capacity of the BIMO DMCcompared to that of the equivalent BSC obtained in caseof on/off detection is shown in Fig. 3 as a function of themean photon number N c and for ∆ = 0 , . , while in Fig. 4the BIMO DMC is compared to the equivalent BSC for N c = 1 , , , as a function of the phase diffusion parameter ∆ . It is possible to observe that a higher capacity can beobtained by the BIMO DMC with respect to the equivalentBSC, that may possibly lead to improved BER improvementwhen an error correction code is applied to the two channels.This aspect is indeed investigated in the next section. Thecapacity improvement offered by the photon counting detectordecreases as N c increases, in particular for low values of ∆ ,as it can be observed by both Fig. 3 and Fig. 4. C l a ss i c a l c apa c i t y o f B I M O , D e l t a = , . BIMO Delta=0BSC Delta=0BIMO Delta=0.5BSC Delta=0.5
Figure 3. Classical capacity of the equivalent BSC with cross-over probabilityQBER (dashed curves) compared to that of the BIMO DMC (solid curves)for ∆ = 0 (circle) and ∆ = 0 . (triangle) as a function of mean photonnumber N c . V. BER PERFORMANCE IN PRESENCE OF FECThis section investigates the performance obtainable withForward Error Correction (FEC) codes applied to the schemeof Figs. 1 and 2. The m -bits codeword of a systematicFEC code with code rate R c is generated concatenating L information bits and r redundancy bits so that m = L + r and R c = L/ ( L + r ) .A systematic low density parity check code has beenselected as test FEC code, due to its capacity achieving perfor-mance (albeit at very large block lengths) and low complexityiterative decoding structure, and a simulation analysis has beenperformed to assess the potential performance improvements OURNAL OF L A TEX CLASS FILES 5 C l a ss i c a l c apa c i t y o f B I M O f o r d i ff e r en t N c BIMO Nc=1BSC Nc=1BIMO Nc=3BSC Nc=3BIMO Nc=7BSC Nc=7BIMO Nc=12BSC Nc=12
Figure 4. Classical capacity of equivalent BSC with cross-over probabilityQBER (circle) and of BIMO DMC (triangle) for N c = 1 , , , as afunction of the phase diffusion parameter ∆ . obtainable using the soft-metric of Eq. (8). Three differentquantum channel models have been considered, all with thesame equivalent uncoded raw BER value, that will be denotedas QBER. The simulation results are shown in Fig. 5, whereeach pair of BER-FER curves depicts the residual bit error rateand frame error rate after channel decoding. The followingparameters have been considered: • R c = 0 . , L = 500 , r = 500 , • R c = 0 . , L = 252 , r = 156 , • R c = 0 . , L = 750 , r = 250 .The black curves in Fig. 5 labeled ”Q-BSC” are associatedwith an equivalent BSC with binary input X = k , binary out-put Y and transition probability QBER derived from Eq. (15)(i.e. a receiver that does not use the additional informationderived from the knowledge of n and n and simply performson/off detection) with LLR values [26]:LLR ( Y ) = log (cid:20) P ( Y = 1 | X ) P ( Y = 0 | X ) (cid:21) = log (cid:16) − QBERQBER (cid:17) , if X = 1;log (cid:16) QBER − QBER (cid:17) , if X = 0 . The blue curves labeled as “Q-AWGN” represent the per-formance obtainable over a fictitious Additive White Gaus-sian Noise (AWGN) channel model with a Signal to NoiseRatio (SNR) selected in order to achieve an uncoded biterror probability QBER with a binary antipodal scheme. Thecurves labeled as “Q-BIMO” represent the main result andare obtained transmitting through the BIMO DMC quantumchannel model shown in Fig. 2 with equivalent uncoded biterror probability QBER and using as input soft-metrics for theLDPC decoder, the LLR values generated via photon countingaccording to Eq. (8).As it is apparent from the results for the photon countingreceiver, the BER and FER performance largely improve whenthe BIMO DMC and the LLR metrics from Eq. (8) are
Figure 5. Simulated BER and FER values for a LDPC code with L =500 , r = 500 and R c = 0 . (top plot), L = 252 , r = 156 and R c = 0 . (center plot) and L = 750 , r = 250 and R c = 0 . (bottom plot), obtainedwith different models of the quantum channel: BSC (Q-BSC curves, black),AWGN (Q-AWGN curves, blue) and BIMO DMC (Q-BIMO curves, red). employed instead of the simpler BSC metrics. As an example,in the upper plot in Fig. 5 for QBER = 0 . the BIMODMC with soft-metric processing offers almost three ordersof magnitude improvement in BER with respect to the BSC OURNAL OF L A TEX CLASS FILES 6 model and the associated hard-metric processing. We mustnote that the curves labeled as “Q-AWGN” must only beused as reference, since with the small number of photonswe considered in our simulations the AWGN channel modelwould not be appropriate.A comparison among the residual FER and BER valuesobtainable with the considered channel models for LDPCcodes with code rates . (center plot) and . (bottom plot)is shown in Fig. 5. Also in these cases, both FER and BERvalues improve up to several orders of magnitude when usinga photon counting receiver and the associated LLR values.Furthermore, we can observe that as the code rate increases,the “Q-BIMO” performances obtained with BIMO LLR met-rics get closer to the “Q-AWGN” performances obtained withclassic AWGN LLR metrics (although, as mentioned before,the AWGN model is not applicable in case of low number ofreceived photons).Fig. 6 compares the BER values obtained with the BSC andthe BIMO channel models for different code rates, showingthat, as expected, for higher rates, a lower QBER value isrequired before significant coding gains can be observed. Figure 6. Simulated residual BER obtained with BSC (Q-BSC curves, black)and BIMO DMC (Q-BIMO curves, red) models of the quantum channel andLDPC codes with different code rates ( R c = 0 . , . and . ). ¿From Fig. 7, we can observe that for high values of N c (i.e. at low values of QBER) the BIMO DMC model can beapproximated with an AWGN model, while the AWGN modelapproximation may be unreliable at high QBER (low N c )values, in particular at lower code rate values. Finally, Fig. 8shows the residual BER obtained on the BIMO channel byLDPC codes with code rate R c = 0 . , . , . for differentvalues of N c . VI. C ONCLUSIONS
In this paper a photon-number-assisted, polarization-basedbinary transmission scheme equipped with a low-complexityphoton counting receiver has been considered, analyzing bothits capacity and its BER performance in presence of ca-pacity achieving low density parity check codes. Differentchannel models applicable to the considered transmission
Figure 7. Simulated residual BER obtained with AWGN (Q-AWGN curves,blue) and BIMO DMC (Q-BIMO curves, black) models of the quantumchannel and LDPC codes with different code rates ( R c = 0 . , . and . ).Figure 8. Simulated residual BER for LDPC codes with R c = 0 . , . , . over BIMO DMC as a function of the mean photon number N c . scheme have been compared, proposing a time varying binary-input/multiple-output model and evaluating its LLR metricsand channel capacity. It has been shown how the BIMOchannel model outperforms the corresponding BSC model,by taking full advantage of the additional information offeredby the photon counting detector. It was also shown that,as expected, the advantage offered by the photon countingdetector deceases as the mean photon number N c increases,and that the BIMO model can be approximated by an AWGNmodel at low values of QBER, i.e. for high values of N c .A CKNOWLEDGMENT
This work was supported by MIUR (grant FIRB “LiCHIS”- RBFR10YQ3H) and NATO (SfP project 984397 ”SecureQuantum Communications”).
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Marina Mondin is Associate Professor at Dipartimento di Elettronica,Politecnico di Torino. Her current interests are in the area of signal processingfor communications, modulation and coding, simulation of communicationsystems, and quantum communication. She holds two patents. She has beenAssociate Editor for IEEE Transactions on Circuits and Systems-I from 2010to 2013 and has been in the 2012 TCAS committee for the selection ofthe Darlington and Guillemin-Cauer Best Paper Awards. She is currentlycoordinating the NATO SfP project “Secure Communication Using QuantumInformation Systems”. She is author of more than 150 publications.
Fred Daneshgaran received the Ph.D. degree in electrical engineering fromUniversity of California, Los Angeles (UCLA), and since 1997 has beena full Professor with the ECE Department at California State University,Los Angeles (CSLA). From 2006 he serves as the chairman of the ECEdepartment. Dr. Daneshgaran is the founder of Euroconcepts, S.r.l, a R&Dcompany specializing in the design of advanced communication links andsoftware radio that operated from 2000 to 2010. From 1999 to 2001 he wasthe Chief Scientist and member of the management team, for TechnoConcepts,Inc. where he directed the development of a prototype software defined radiosystem, managed the hardware and software teams and orchestrated the entiredevelopment process. He is the director of the fiber and non-linear opticsresearch laboratory at CSLA, and served as the Associate Editor of the IEEETrans. On Wireless Comm. in the areas of modulation and coding, multirateand multicarrier communications, broadband wireless communications, andsoftware radio, from 2003 to 2009. He has served as a member of theTechnical Program Committee (TPC) on numerous conferences. Most recentcontributions include IEEE WCNC 2014, CONWIRE 2012, ISCC 2011 to2014, and PIMRC 2011.
Inam Bari
Inam Bari obtained his BS in Telecommunication Engineeringfrom the National University of Computer and Emerging Science (NUCES-FAST), Pakistan in 2007, and was awarded bronze medal. In 2008, hewas awarded a full 5 years MS leading to PhD scholarship by the HigherEducation Commission of Pakistan. He obtained his MS and PhD degreesfrom Politecnico di Torino, Italy, and is currently Assistant Professor atNUCES-FAST, Peshawar, Pakistan.
Maria Teresa Delgado received her BS Degree in Electrical Engineering atthe Universidad Central de Venezuela in Caracas, Venezuela in 2006, and herMS and Ph.D. degrees in Telecommunication Engineering from Politecnicodi Torino, Italy, in 2008 and 2012. Her interests are in the area of signalprocessing for telecommunications, coding, simulation of communicationsystems, quantum cryptography and physical layer security for wirelessand quantum communication systems. She is currently researcher at IstitutoSuperiore Mario Boella, Turin, Italy.
OURNAL OF L A TEX CLASS FILES 8
Stefano Olivares received the Ph.D. degree in Physics from the Universityof Milan, Milano, Italy, and is currently a Researcher at the Department ofPhysics, University of Milan, Italy. He is a theoretician and his interestsinclude quantum information, quantum estimation, quantum optics, quantuminterferometry and quantum computation. His main contributions are in thefields of quantum estimation of states and operations, generation and applica-tion of entanglement, quantum information, communication and decoherence.Although his research activity is mainly theoretical, he is an active collaboratorin many experimental groups. He is author of about 100 publications.
Matteo G. A. Paris received his Ph.D. in physics from University of Pavia,and is currently professor of quantum information and quantum optics at theDepartment of Physics of the University of Milan. His main contributionsare in the fields of quantum estimation of states and operations, quantumtomography, generation, characterization and application of entanglement,quantum interferometry, nonclassical states and open quantum systems. Inthese fields he is author of about 250 publications in international journals.From 2013 he is editor-in-chief of