Reversible Hardware for Acoustic Communications

1 Re v ersible Hardware for Acoustic Communications Harun Siljak, Member , IEEE, Julien de Rosny , Member , IEEE and Mathias Fink Abstract —Reversible computation has been recognised as a potential solution to the technological bottleneck in the future of computing machinery . Rolf Landauer determined the lower limit for power dissipation in computation and noted that dissipation happens when inf ormation is lost, i.e., when a bit is erased. This meant that rev ersible computation, conserving information conserves energy as well, and as such can operate on arbitrarily small power . There wer e only a few applications and use cases of re versible computing hard ware. Her e we present a novel re versible computation architecture for time rev ersal of waves, with an application to sound wa ve communications. This energy efficient design is also a natural one, and it allows the use of the same hardware f or transmission and reception at the time re versal mirror . Index T erms —rev ersible computation, cir cuit design, wa ve time re versal, wireless communications I . I N T RO D U C T I O N T HE majority of computation we perform is irreversible: addition of two numbers, or logical AND of two bits both destroy the information about the inputs. In a computation paradigm which prioritises saving memory resources, losing information is a consequence of using a register for something else as soon as its current content is used for the last time. The arithmetic units are often designed so that the result replaces one of the input operands, and this is considered an important sav e in resources. Somewhat paradoxically , the call for reversibility and preserv ation of information through the computation process also comes from the resource optimiza- tion perspective. Thermodynamics of computation explains the mechanisms of energy use and dissipation in computing systems. Landauer [1] established an important lo wer limit for computation energy dissipation: the erasure of one bit takes a fraction of a joule, energy proportional to the working temperature of the system (with the proportionality coef ficient equal to the product of the Boltzmann constant and natural logarithm of two). This lo wer limit follo ws from the equiv alence of thermodynamical and informational entropy and, at the time, it was significantly lower than the limits imposed by techno- logical (semiconductor) constraints. With the advancement of semiconductor industry , the limits of de vices became closer to Landauer’ s limit. Landauer’ s limit bounds bit erasure: This publication has emanated from research supported in part by a research grant from Science F oundation Ireland (SFI) and is co-funded under the European Regional Development Fund under Grant Number 13/RC/2077. The project has recei ved funding from the European Unions Horizon 2020 research and innov ation programme under the Marie Skodowska-Curie grant agreement No 713567 and was partially supported by the COST Action IC1405. Harun Siljak is with CONNECT Centre, T rinity College Dublin, Ireland, e-mail: siljakh@tcd.ie. Julien de Rosny and Mathias Fink are with Institut Langevin, ESPCI ParisT ech, CNRS UMR 7587, 75231 Paris Cedex 05, France, e-mails: {julien.derosny ,mathias.fink}@espci.fr. operations that do not erase information (bits) do not hav e a lower bound in thermodynamical-informational sense. This fact qualifies information-conserving computation as a poten- tial solution for the future of general computing in the post- Moore law era. The concept of re versible computation, rev ersible logic gates and circuit design hav e been a topic of research since Bennett’ s pioneering work [2] on applying Landauer’ s ideas to hardware. Howe ver , there ha ve been almost no applications of rev ersible circuits to real world problems, no interfaces with the nature and other technology . In this paper , we present a case for employing rev ersible computation in wav e time reversal, using acoustic underwater communication as a working example. The case of acoustic communications based on wa ve time rev ersal is a good ground for rev ersible computation. Every- thing is reversible: the communication scheme re versing the carrier wav e tow ard the original source and the en vironment obeying re versible Euler equation. Here we show ho w the computation performing all of it can be reversible as well. Of course, wa ve time reversal is not limited to acoustic communication, as it is the basis of a beamforming approach for RF communications. Hence, our contribution is relev ant to multiple wireless communications paradigms. Our motiv ation for presenting the rev ersible hardware solution for wave time rev ersal as a contribution to communications stems from here: a solution for time-re versal massi ve MIMO would be an adaptation of the one presented here, and same holds for optical communications based on time re versal. In this manner , digital signal processing in communications would be ready for the post-Moore age of rev ersible and/or quantum computing. T ime-re versal based communications implemented with this circuitry then have both the potential of immense energy ef ficiency and a chance to become the natural solution for the physical layer of quantum networks of the future. W e begin by re visiting the mechanism of wa ve time rev ersal, followed by a presentation of reversible computation and motiv ation of its use. W e discuss the possible design options employing reversible hardware for time re versal and sho w design results. W e conclude with a discussion of the proposed solution, future research and the wider effect of re versible hardware introduction in wireless communications. I I . R E V E R S I B I L I T Y O F W A V E S A N D C O M P U TA T I O N It is not a coincidence that we chose wa ve time re versal for the demonstration of an efficient rev ersible hardware applica- tion. As this section will show , the wa ve time reversal and rev ersible computation both rely on keeping the information about backtracking known, to run backwards. They share the same philosophy and a common foe. 2 Fig. 1. The w av efront distorted by heterogeneities comes from a point source and is recorded on the cavity elements. In the next step the recorded signals are time-reversed and re-emitted by the elements. The time-rev ersed field back-propagates and refocuses exactly on the initial source.[3] A. W ave T ime Reversal Both, rev ersing waves and re versing computation are plagued with the scale destroying reversibility . While at the microscale the elementary components of the system are obey- ing re versible laws (be it simple computational operations, be it equations of motion), their ensembles lose the rev ersibility at the macroscale. Loschmidt’ s thought experiment with a deamon capable of reversing all velocities of particles in a gas and hence rev ersing the behaviour of the ensemble asks for too much information and ability on the deamon’ s side, but it is a worth y goal to pursue: ho w can we rev erse a propagating wa ve so it ends up con ver ging at its original source? The solution based on time reversal mirrors (TRMs) [4] performs this regardless of the comple xity of the medium as if time were going backwards, and has been implemented with acoustic, electromagnetic and water waves. It requires the use of emitter–receptor antennas positioned on an arbitrary enclosing surface. The wa ve is recorded, digitized, stored, time-rev ersed and rebroadcasted by the same antenna array . If the array intercepts the entire forward wav e with a good spatial sampling, it generates a perfect backward-propagating copy . The principle of wa ve time rev ersal builds upon the exact nature of the wa ve equation, and its solution being a continu- ous function of three spatial and one temporal dimension, i.e. described over a hypervolume with four variables, bounded by a hypersurface with three variables. This boundary can either be observed as composed of three spatial dimensions or of two spatial and one temporal dimension . Depending on the choice of the boundary description, we ha ve two dif ferent approaches to time rev ersal, dubbed “à la Huygens” (named after Huygens integral theorem) and “à la Loschmidt” (named after Loschmidt’ s deamon). [3] 1) The time-r ever sal mirr or appr oach ‘à la Huygens’: In this approach, represented in the Fig. 1, a transient wavefield originating from the initial source is radiated throughout a heterogeneous medium closed in a cavity bounded by a two- dimensional surface. This surface is populated with sensing and recording devices keeping the information about the wa vefield and its normal deriv ati ve. This process continues until the incoming field v anishes along the boundary . This recording suffices for the recovery of the wav efield, as we will soon see. Out of the two solutions of the wav e equation (wave operator obeys time-re versal symmetry), the causal one is radiated from the source, and we aim to radiate the anti-causal one from the boundary . The collected samples are hence time- rev ersed and rebroadcasted by the same antenna array that has collected them. This new wav e satisfies a homogeneous wav e equation with the time-re versed boundary conditions without the original source. Hence it is not enough to time-rev erse the wav efield on the boundary , as the original source needs to be rev ersed into a sink. While returning to the original source, the re-emitted wa ve does appear to conv erge, but as it cannot stop on its own, after the collapse it continues to propagate in div ergent manner . T o compensate this diver ging field, we either use an activ e source at the focusing point canceling the field, or a passiv e sink as a perfect absorber . [5] So f ar , we assumed the idealised case where the entire surface of the boundary is covered with transceiv ers, which requires a large number of hardware components. This re- quirement can be dropped, and the ex ecution of the rev ersal can be simplified. One way is locating the TRM in the far field of the source and of the medium heterogeneities. This halves the quantity of data to be stored, as the normal deriv ati ve remains proportional to the field and does not ha ve to be recorded at all. In addition to this, it was experimentally shown that TRM consisting of a small number of elements (time-rev ersal channels) functions on a limited angular area as well, when it uses complex en vironments to appear wider than it is. The resulting refocusing quality does not depend on the TRM aperture. In that regard, observe the following experiment setup.[6] A point-like transducer is separated from a TRM by a large distance (much larger than the wav elength) and by a multiple scattering medium (forest of steel rods) and shown in Fig. 2. After emitting a short pulse from the source, the sensors at the TRM collect the impulse response. The spread of these impulse responses is two orders of magnitude higer than the initial pulse duration as the multi-scattering medium is highly diffusi ve. As explained before, in the next step the responses are flipped in memory and re-transmitted from the TRM. The impulse duration, reconstructed at the original source is the same as the original; the spatial spread is a level of magnitude smaller (i.e. more coherent) when the propagation happens in the complex medium, than in the case of free space propagation. 2) The instantaneous time mirr or appr oach ‘à la Loschmidt’: Going back to Loschmidt’ s demon a ble to turn the direction of particles instanteneously , if one decides to imitate it, unlike the Huygens case, the measurements of the incoming wavefield have to be performed at one specific time in the whole volume. At that point a new set of initial conditions is imposed, in which the sign of the time deriv ati ve is reversed, and the resulting wa ve is the time-rev ersed original. Examine a case of a bath of fluid, placed on a shaker to control its vertical motion. After emitting a pulse from a 3 Fig. 2. T ime-rev ersal experiment through a diffusi ve medium [3] point on the fluid surface, at the chosen time instant a vertical downw ards acceleration is applied to the bath, an impulsiv e change of wave celerity which can be described by a delta function in time. While the propagation of the initial outwards propagating wa ve is not affected, a ne w contribution emerges: a backwards con ver ging circular wav e packet. Just like in the Huygens case, this wav e packet focuses at the original source and proceeds di ver ging afterwards. While the result is the same, we note that in this case no transcei vers or memory elements were used: the information is stored in the medium itself. The Bridge to Computing Among time re versal studies that ha ve follo wed the dev elop- ment of these concepts one creates a link between computation and time reversal in wav es [7]. A dissipativ e chaotic system consisting of a drop bouncing on a vibrated liquid bath, exchanging information with the wa ves it forms, can be rev ersed. The elementary motions performed by the system are equiv alent to writing, storing, reading and erasing operations of a Turing machine. The bouncing drop reads information as it backtracks, at the same time it is erasing the read information. In the next section, we in vestigate computational systems which use an equiv alent principle to perform useful calculations and save power . B. Rever sible Hardwar e Landauer f amously concluded that “the information is physical” and brought together Shannon’ s and Boltzmann’ s views on entropy . [1] Digital computation that does not lose information (erase bits of information), does not hav e to dissipate po wer . When we delete a bit, the information that was stored there physically moves to the environment in form of heat, a direct display of Boltzmann’ s thermodinamical entropy . None of it would have to be dissipated from the entropical perspectiv e if the erasure was not performed. Observe a digital circuit consisting of logical gates: e.g. a single AND gate with its two inputs and one output. Its output is one when both inputs are one simultaneously; otherwise it is zero. Hence the knowledge about the output is not enough to tell us the inputs, as three different input combinations collapse into one output state. If we want to make an information- preserving gate, it has to hav e a one-to-one correspondence between output states and input states. This asks for the same number of outputs and inputs in such re versible gates . T wo reversible bit operations are bit in version and swap of two v ariables. T o make more use of them, we devise gates controlling these operations according to the state of other variables. Fig. 3 shows some basic rev ersible gates as part of larger reversible circuits: all circuits in the figure are built using Feynman and Fredkin gates. Feynman gate is a controlled NOT : the variable with the ⊕ is in verted if and only if the control input, the variable with • is equal to 1. In a more general setting of the T offoli gate, multiple variables can control a single NOT ; in that case the function controlling the gate is an AND of the control inputs. Similarly , the Fredkin gate swaps the variables joining in the × if and only if the variable(s) with • are equal to 1. These gates enable design of re versible circuits which perform the usual digital electronics tasks. A full adder [8] and D-latch [9] are sho wn in Fig. 3. Additional inputs/outputs are auxilliary variables–the ancilla bits . In the D-latch example, the 0 bit and the Feynman gate attached to it are necessary to copy the latch output for feedback, as rev ersible circuits do not allow fan-out (it violates the one-to-one correspondence requirement). Most classical computation is irrev ersible, re-using the memory by often removing intermediate results. In the past, most of the dissipation in logic circuits came from imper- fections of the practical implementation. W ith the progress of semiconductor technology , the dissipation lev els are approach- ing those of Landauer’ s limit, and reversibility is gaining importance. As Moore’ s law comes to its potential end, and alternativ e solutions are sought, one of the candidates being rev ersible computing. Irrev ersible calculations could be easily embedded in a reversible computation by merely keeping track of the steps made. T o mitigate the need for unbounded memory , Bennett [2] introduced a trick: if a computation is made in a rev ersible circuit in one direction and then in reverse (computed, and then uncomputed), the memory occupied in the direct pass is freed in the return pass, and it is available for a new computation without bit erasures, and entropy is not increased (the memory after the return pass is back to the state before the direct pass). The lack of application for reversible computation in the classical realm is rev ersed in the quantum computing domain. Most quantum computing schemes require re versibility to operate, so the rev ersible logic gates are constituent parts of quantum circuits (and are often referred to as quantum gates ). Rev ersible computation is not limited to electronics (where adiabatic cir cuits are known for several decades [10]) and quantum computers: (micro)electromechanical systems and quantum dots are also capable of reversible computation. I I I . T H E D E S I G N W e have seen so far a computational paradigm relying on reversibility of calculation, and a communication scheme relying on the reversibility of wav e propagation. In this part of the article, we proceed with designing a TRM based on rev ersible hardware. The rev ersible gates will form the digital 4 Fig. 3. Reversible circuits: D-latch, full adder , and logical gates as building blocks logic part in the TRM, but the design is more complex than just digital logic. With Fig. 4 we illustrate the layers of the design task: 1) The en vironment is rev ersible to an extent. In the use case of acoustic underwater communication, the physics of wav e propagation in water is reversible, but the issues arise as we lose information in the process: parts of the wa ve might end up reflected to unreachable parts of the en vironment if the observed space is not ergodic, guaranteeing all parts of the environment to be visited by the wav e components. The hardware in contact with the en vironment are the microphones and speakers, i.e. sensors and actuators. 2) The analog computation part of the TRM loses informa- tion. It comprises of anti-alias filters before analog-to- digital con version (ADC), filters after digital-to-analog con version (D AC), amplifiers accompanying the filters and the con verters themselves, at the transition to the digital domain. W e analyse these components in Section III-A. 3) Finally , the digital computation part of the TRM is rev ersible and no increase in entropy is necessary . This part entails writing in memory and unwriting, in the fashion of Bennett’ s trick, enabling reuse of memory for the next incoming wav e, while not increasing the entropy . It may include a transform into frequency domain and digital filtering, and we discuss these options as well in Section III-B. Fig. 4. The classical (top) and the rev ersible solution (bottom) for the classical time reversal chain. A. Analog pr ocessing Analog processing is the lossy , inherently irrev ersible bridge between two domains which exhibit rev ersibility: the physics of wave propagation and the digital signal processing chain we introduce. Our main goal at this point is to make the mechanisms in this part of the processing chain bidirectional, so that they can be used both for the inputs and the outputs. Howe ver , we are interested in saving as much information as we can, so we inv estigate the information loss in this part of the chain as well. 1) Bidir ectional amplification and AD/D A con version: From the information-preserving perspective, ideal amplifica- tion is not an interesting process. Howe ver , the real amplifier is an imperfect device with a limited bandwidth and it loses signal information and introduces changes in the signal shape. It requires additional energy for the signal, hence we hav e to allocate a non-zero energy budget for this part of the computation. At the same time, the analog to digital and digital to analog con verters both modify the signal they con vert due to finite resolution and sampling rates, losing information about the original signal. Ho we ver , the idea of the single de vice performing as both an ADC and a D AC depending on the direction exists both in academia and industry , with a large number of patents describing these bi-directional devices. [11] In our proposed solution, we assume that the bi-directional con verters are bundled with bi-directional amplifiers [12]. W e note the complexity of structure and switching in these devices. 2) The information-increasing filter: A part of analog to digital con version is the anti-aliasing filter . Filtering, in the most common interpretation, removes a part of the signal and hence loses information about the original signal. How- ev er, the anti-aliasing filter is employed to prevent significant information loss due to spectrum ov erlaps in the analog-to- digital conv ersion, and hence in this situation represents an information gain and may be re-interpreted in the context of useful, r elevant information [13]. T o avoid confusion, we may consider the anti-aliasing filter as a part of the analog-to- digital con verter and as such, implement it in the bi-directional fashion. 3) One-bit re versal: The con version is additionally simpli- fied in the one-bit solution [14] where the receiv ers at the mir- ror register only the sign of the wav eform and the transmitters emit the reversed v ersion based on this information. It is a spe- cial case of analog-to-digital and digital-to-analog conv ersion with single bit con verters. The reduction in discretisation le vels also means simplification of the processing chain and making its reversal (bi-directi vity) even simpler . The question of the information loss is not straightforward: while the information about the incoming wa ve is lost in the conv ersion process (and the loss is maximal due to minimal resolution), spatial and temporal resolution are not significantly degraded. This scheme can also be called “one-trit” rev ersal: there are three possible states in the practical implementation: positiv e pressure, negati ve pressure, and ’off ’. Reversibility and multi- valued logic were going hand in hand from the beginning: binary rev ersible logic is just a special case of multi-valued rev ersible logic. Hence, this scheme is readily implementable in reversible logic as well. 5 B. Digital pr ocessing W ith the functionalities rev ersible gates presented in Section II-B can offer when combined into logical circuits, building a digital signal processing chain for wav e time re versal becomes the matter of combining circuits into more complex structures, akin to traditional circuit design. The idea we sho w here can easily be translated into any scheme of modulation- demodulation, coding-decoding, which are often seen in com- munications hardware and softw are. While fully functional and directly applicable, our time rev ersal signal processing chain is a proof of concept for rev ersible communications signal processing of arbitrary complexity . 1) T ime domain r ever sal: The first, straightforward way of performing time reversal of a digitally sampled wav e is storing it in memory and reading the samples in the re verse order (last in, first out, LIFO), analoguous to storing the samples on the stack. The design of re gisters in rev ersible logic is a well- explored topic [9] and both serial and parallel reading/writing can be implemented. In the sense of already presented circuits, we have seen a design for the D-latch (Fig. 3): a combination of latches makes a flip-flop, and a series of flip flops makes a register (and a rev ersible address counter). In the case of wa ve time re versal, this is important to kno w , as the two possible variants of wav e time rev ersal can be interpreted as two variants of memory writing: 1) W av e reversal à la Loschmidt is a large register being loaded in parallel with wav e data; 2) W av e reversal à la Huygens is a lar ge re gister being loaded serially with wav e data. In the case of a localized time reversal mirror (all samples at the same place) m bits from the ADC are memorised at the con verter’ s sample rate inside a k × m bit re gister matrix (where k is the number of samples to be stored for time reversal). In the receiving process, the bits are stored, in the transmission process they are unstor ed , returning the memory into the blank state it started from (uncomputation). W e utilise Bennett’ s trick and lose information without the entropic penalty: the information is kept as long as it is relev ant. 2) F r equency domain r eversal: When additional signal processing, e.g. filtering or modulation is performed, it is con venient to reverse wav es in frequency domain: there, time domain reversal is achieved by phase conjugation, i.e. changing the sign of the signal’ s phase. The transition from time to frequency domain (and vice versa) in digital domain is performed by the Fast Fourier Transform (FFT) and its in verse counterpart. These procedures are inherently re versible and information-preserving, and their implementation in reversible digital circuits asks for a network of rev ersible adders (and rev ersible multipliers, again comprised of adders) [8], and we hav e already seen an implementation of a reversible adder in Fig. 3. The necessary phase conjugation is an arithmetic operation of sign rev ersal, again perfectly reversible and with a known implementation. The additional signal processing can be performed reversibly as well: one example is the filtering process done through filter banks and wavelet transforms. It remains reversible as all components of signals are preserved, if nothing then as the remainder [15]. Both the rev ersible wa velet computation and re versible Fast F ourier T ransform use the lifting scheme. 0 bit resolution 10 0 500 100 waiting time 1000 80 bit erasures 60 1500 40 20 20 2000 0 2500 Irreversible implementation in the frequency domain Irreversible implementation in the time domain Reversible implementations (a) 0 bit resolution 10 50 100 waiting time 100 80 information loss 60 150 20 40 20 200 0 250 reversal in a chaotic cavity reversal in a complex medium (b) Fig. 5. Information loss in (a) digital and (b) analog part of the system. Units are omitted as the particular aspects of implementation are not relevant for the illustration of effects. Plot (a) is obtained by counting operations, plot (b) by simulation of back-scattering, both originating from theoretical calculations. I V . D I S C U S S I O N A N D C O N C L U S I O N S W e have presented the components to be used in the implementation: where possible (in the digital domain) we use rev ersible circuits, otherwise we use bidirectional components. What is the gain of the ne w implementation? As already suggested, the loss of information is directly related to the dissipation of energy in the system, so let us observe how does our solution fare in this regard. Fig. 5(a) is a comparison of the bit erasures in different implementations of the digital circuitry: frequenc y domain (FFT) and time domain rev ersal performed by irreversible circuits, compared to reversible implementations. The num- ber of erasures changes depending on two parameters: bit resolution of the ADC and the waiting time–the length of the interv al in which samples are collected before re versal starts, equi v alent to the number of digitised samples. The increase in both means additional memory locations and additional dissipation for irrev ersible circuits. The irre versible FFT implementation has an additional information loss caused by additional irrev ersible circuitry compared to the irreversible time domain implementation. Our implementation has no bit erasures whatsoever . The price that is paid reflects in the larger number of gates used in the circuit: the number of gates has only spatial consequences, information-related energy dissipation is zero thanks to information conservation. 6 Having no bit erasures means theoretical decrease in energy consumption proportional to the number of bits erased by the state of the art irre versible implementations–multiplied by the number of processing chains serving multiple transcei vers, it is clear that this quantity , as small as it may seem in the case of a single transceiver , is indeed significant, especially in the near future where the Landauer limit becomes the dominant bound in semiconductor component power dissipation. As the circuits in our solution perform arithmetical and logical operations in the same vein as irrev ersible circuits in the state of the art implementations, the performance of the two solutions is the same in terms of results (the components are validated at the lev el of logical circuits). On the other hand, in Fig. 5(b) we see the information loss in the analog part of the system, and we differentiate two typical en vironments, the chaotic cavity and the complex medium. The chaotic cavity is an ergodic space with sensi- tiv e dependence on initial conditions for waves. In such an en vironment there is little to no loss in the information if the waiting time is long enough and the ADC resolution is high enough. The complex medium is one with a large number of scatterers; In such media, the difference is caused by some of the wave components being reflected backwards by the scattering en vironment, hence not reaching the TRM. Again, more information is retained with the increase in the ADC resolution. Howe ver , as reported in [14], the information loss from lo w-resolution ADC use does not af fect the performance of the algorithm. The analog part of the scheme remains a topic of our future work, as it leav es space for improvements of the scheme. When the first prototype of a re versible FFT chip was introduced [8], it was shown that the implementation based on 8-bit adders and 11-bit multipliers requires 40,000 transistors. As the idea of information and energy conserv ation in com- putation allows for very dense packing (no heat dissipation to limit the density), this order of magnitude for our solution is acceptible (the rest of the circuitry we introduce in the chain needs two or three orders of magnitude fewer transistors), and if we opt for no frequency domain processing, i.e. just using memory , we can perform the task with less than 1,000 transistors. In this first application of rev ersible hardware to a physical process we have demonstrated the complementary nature of wa ve rev ersal and computational re versal which can be put to use. Our implementation of wa ve time re versal using re versible hardware carries the promise of reduced power consumption, and it also fits in the bigger picture: in this vision of the future, all computation is reversible, no matter if it is performed on classical or quantum basis. This solution is just the first step in the proliferation of re versible computation in communications. The inherent rev ersible properties of communications, including but not limited to channel reciprocity and transmitter-recei ver duality , make communications technology an area with a lot of poten- tial in reversible computation. W ith the inevitable penetration of quantum-based techniques in communications, this link with rev ersible computation grows stronger and needs to be thoroughly inv estigated. 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Kudo, “Redefined block-lifting-based filter banks with efficient rev ersible nonexpansive con volution, ” IEEE T ransactions on Circuits and Systems for V ideo T echnology , vol. 29, no. 5, pp. 1438–1447, 2018. Harun Siljak (M ’15) graduated from Automatic Control and Electronics Department, University of Sarajev o (BoE 2010, MoE 2012) and International Burch University Sarajev o (PhD 2015). Currently he is a postdoctoral Marie Curie Fellow at CONNECT Centre, Trinity College Dublin, working on rev ersible computation, complex and nonlinear dynamics in wireless com- munications. Julien de Rosny receiv ed the M.S. Degree and the Ph.D. degree from the Univ ersity UPMC, Paris, France in 1996 and 2000, respectively , in wave physics. He was a postdoctoral researcher at Scripps Research Institute, Cal- ifornia, USA, in 2000-2001. In 2001, he joined CNRS at Laboratoire Ondes et Acoustique, France. Since 2014, he is a CNRS senior scientist at Institut Langevin, Paris, France. His research interests include telecommunications in complex media, acoustic and electromagnetic wav es based imaging. Mathias Fink is the George Charpak Professor at ESPCI Paris where he founded in 1990 the Laboratory “Ondes et Acoustique” that became in 2009 the Langevin Institute. He is member of the French Academy of Science and of the National Academy of T echnologies of France. In 2008, he was elected at the College de France on the Chair of T echnological Innov ation. His area of research is concerned with the propagation of waves in complex media and the dev elopment of numerous instruments based on this basic research. His current research interests include time-reversal in physics, wav e control in complex media, super-resolution, metamaterials, multiwave imaging, geophysics and telecommunications. He holds more than 70 patents, and has published more than 400 peer revie wed papers and book chapters. 6 start-up companies with more than 400 employees have been created from his research (Echosens, Sensitive Object, Supersonic Imagine, Time Reversal Communications, CardiaW ave and GreenerW ave).