Scalable optical hypercube-based interconnection network for massively parallel computing

Two important parameters of a network for massively parallel computers are scalability and modularity. Scalability has two aspects: size and time (or generation). Size scalability refers to the property that the size of the network can be increased with nominal effect on the existing configuration. Also, the increase in size is expected to result in a linear increase in performance. Time scalability implies that the communication capabilities of a network should be large enough to support the evolution of processing elements through generations. A modular network enables the construction of a large network out of many smaller ones. The lack of these two important parameters has limited the use of certain types of interconnection networks in the area of massively parallel computers. We present a new modular optical interconnection network, called an optical multimesh hypercube (OMMH), which is both size and time scalable. The OMMH combines positive features of both the hypercube (small diameter, high connectivity, symmetry, simple routing, and fault tolerance) and the torus (constant node degree and size scalability) networks. Also presented is a three-dimensional optical implementation of the OMMH network. A basic building block of the OMMH network is a hypercube module that is constructed with free-space optics to provide compact and high-density localized hypercube connections. The OMMH network is then constructed by the connection of such basic building blocks with multiwavelength optical fibers to realize torus connections. The proposed implementation methodology is intended to exploit the advantages of both space-invariant free-space and multiwavelength fiber-based optical interconnect technologies. The analysis of the proposed implementation shows that such a network is optically feasible in terms of the physical size and the optical power budget.     

Experimental demonstration of the optical multi-mesh hypercube: scaleable interconnection network for multiprocessors and multicomputers

A prototype of a novel topology for scaleable optical interconnection networks called the optical multi-mesh hypercube (OMMH) is experimentally demonstrated to as high as a 150-Mbit/s data rate (2(7) - 1 nonreturn-to-zero pseudo-random data pattern) at a bit error rate of 10(-13)/link by the use of commercially available devices. OMMH is a scaleable network [Appl. Opt. 33, 7558 (1994); J. Lightwave Technol. 12, 704 (1994)] architecture that combines the positive features of the hypercube (small diameter, connectivity, symmetry, simple routing, and fault tolerance) and the mesh (constant node degree and size scaleability). The optical implementation method is divided into two levels: high-density local connections for the hypercube modules, and high-bit-rate, low-density, long connections for the mesh links connecting the hypercube modules. Free-space imaging systems utilizing vertical-cavity surface-emitting laser (VCSEL) arrays, lenslet arrays, space-invariant holographic techniques, and photodiode arrays are demonstrated for the local connections. Optobus fiber interconnects from Motorola are used for the long-distance connections. The OMMH was optimized to operate at the data rate of Motorola's Optobus (10-bit-wide, VCSEL-based bidirectional data interconnects at 150 Mbits/s). Difficulties encountered included the varying fan-out efficiencies of the different orders of the hologram, misalignment sensitivity of the free-space links, low power (1 mW) of the individual VCSEL's, and noise.     

Optical binary de Bruijn networks for massively parallel computing: design methodology and feasibility study

The interconnection network structure can be the deciding and limiting factor in the cost and the performance of parallel computers. One of the most popular point-to-point interconnection networks for parallel computers today is the hypercube. The regularity, logarithmic diameter, symmetry, high connectivity, fault tolerance, simple routing, and reconfigurability (easy embedding of other network topologies) of the hypercube make it a very attractive choice for parallel computers. Unfortunately the hypercube possesses a major drawback, which is the complexity of its node structure: the number of links per node increases as the network grows in size. As an alternative to the hypercube, the binary de Bruijn (BdB) network has recently received much attention. The BdB not only provides a logarithmic diameter, fault tolerance, and simple routing but also requires fewer links than the hypercube for the same network size. Additionally, a major advantage of the BdB network is a constant node degree: the number of edges per node is independent of the network size. This makes it very desirable for large-scale parallel systems. However, because of its asymmetrical nature and global connectivity, it poses a major challenge for VLSI technology. Optics, owing to its three-dimensional and globalconnectivity nature, seems to be very suitable for implementing BdB networks. We present an implementation methodology for optical BdB networks. The distinctive feature of the proposed implementation methodology is partitionability of the network into a few primitive operations that can be implemented efficiently. We further show feasibility of the presented design methodology by proposing an optical implementation of the BdB network.     

Reconfigurable time-steered array-antenna beam former

We present and analyze a hardware-optimized technique that provides true-time-delay steering for broadband two-dimensional array-antenna applications. The technique improves on previous approaches by the reduction of the two-dimensional beam-former architecture complexity, by the provision of flexibility in time-delay unit selection, and by the potential reduction of optical loss. The technique relies on a one-dimensional bank of time-delay units to form the required time-delay gradient for proper off-broadside angle steering. A reconfigurable optical interconnection fabric is used to reassign dynamically the connections between the time-delay units and individual array elements of a two-dimensional array to effect the proper steering angle along the off-broadside cone.     

On Generalized Fibonacci Cubes and Unitary Transforms

 We present a new interconnection topology called generalized Fibonacci topology, which unifies a wide range of connection topologies such as the Boolean cube (or hypercube), classical Fibonacci cube, etc. Some basic topological properties of generalized Fibonacci cubes are established. Finally, we developed new classes of the discrete orthogonal transforms, based on the generalized Fibonacci recursions. They can be implemented efficiently by butterfly-type networks (like the Fourier, or the Haar transforms). A generalized Fibonacci cube based processor architecture (generalizing the known SIMD architecture — hypercube processor) can be efficiently used for hardware implementation of the proposed discrete orthogonal transforms. Received: October 31, 1996     

Feasibility study of a scalable optical interconnection network for massively parallel processing systems

The theoretical modeling of a novel topology for scalable optical interconnection networks, called optical multimesh hypercube (OMMH), is developed to predict size, bit rate, bit-error rate, power budget, noise, efficiency, interconnect distance, pixel density, and misalignment sensitivity. The numerical predictions are validated with experimental data from commercially available products to assess the effects of various thermal, system, and geometric parameters on the behavior of the sample model. OMMH is a scalable network architecture that combines positive features of the hypercube (small diameter, regular, symmetric, and fault tolerant) and the mesh (constant node degree and size scalability). The OMMH is implemented by a free-space imaging system incorporated with a space-invariant hologram for the hypercube links and fiber optics to provide the mesh connectivity. The results of this work show that the free-space links can operate at 368 Mbits/s and the fiber-based links at 228 Mbits/s for a bit-error rate of 10(-17) per channel. The predicted system size for 32 nodes in the OMMH is 4.16 mm × 4.16 mm × 3.38 cm. Using 16-bit, bit-parallel transmission per node, the system can operate at a bit rate of up to 5.88 Gbits/s for a size of 1.04 cm × 1.04 cm × 3.38 cm.     

Extensible, Low-Chromatic-Sensitivity, All-diffractive-Optics Relay for Interconnecting Optoelectronic Device Arrays

For free-space optical interconnections between optoelectronic chips to reach commercial realization, the technology must provide high-density optical channels in a simple, inexpensive, and easily aligned package. Although point-to-point connections with microlens pairs can provide densities of several thousand channels per square centimeter, the Gaussian nature of the beams limits the connection range to a few millimeters. We propose an arrangement of microlens pairs with an intermediate relay lens that significantly increases the connection distance. This basic setup can be tiled laterally across large chips to form extensible arrays. The optical design is constructed entirely with diffractive elements because of the low chromatic sensitivity over a range of approximately ?10% around the design wavelength. We derive the lateral positioning error at the image by using a simple ray trace, and we show the effect of Gaussian beams. We experimentally demonstrate the low chromatic sensitivity for a system with an interconnection distance of 64 mm. Finally, we demonstrate the interconnection of two linear arrays of multimode fibers with two adjacent channels operating at data rates of hundreds of megabits per second.     

Incrementally scalable optical interconnection network with a constant degree and constant diameter for parallel computing

A new scalable interconnection topology called the spanning-bus connected hypercube (SBCH) that is suitable for massively parallel systems is proposed. The SBCH uses the hypercube topology as a basic building block and connects such building blocks by use of multidimensional spanning buses. In doing so, the SBCH combines positive features of both the hypercube (small diameter, high connectivity, symmetry, simple routing, and fault tolerance) and the spanning-bus hypercube (SBH) (constant node degree, scalability, and ease of physical implementation), while at the same time circumventing their disadvantages. The SBCH topology permits the efficient support of many communication patterns found in different classes of computation, such as bus-based, mesh-based, and tree-based problems, as well as hypercube-based problems. A very attractive feature of the SBCH network is its ability to support a large number of processors while maintaining a constant degree and a constant diameter. Other positive features include symmetry, incremental scalability, and fault tolerance. An optical implementation methodology is proposed for the SBCH. The implementation methodology combines the advantages of free-space optics with those of wavelength-division multiplexing techniques. An analysis of the feasibility of the proposed network is also presented.     

Effects of dead zones in multiple-quantum-well binary-phase modulators on optical interconnections

We investigate the effects of inactive regions [dead zones (DZ's)] in multiple-quantum-well binary-phase modulators used for free-space dynamic optical interconnection applications. Results, however, have implications for other types of pixelated spatial light modulators (SLM's). To our knowledge, the effects of DZ's in SLM's have not before been thoroughly studied in a context other than optical correlation. We investigate the DZ's (considered to be either opaque or transmissive) as a feature that may be exploited in system design, calculating light efficiency and fidelity as a function of DZ fractional width. It is shown that in particular cases an appropriate choice of DZ width would lead to an optical interconnection with substantially improved cross-talk performance.     

Space-variant interconnections based on diffractive optical elements for neural networks: architectures and cross-talk reduction

Optical architectures for fully connected and limited-fan-out space-variant weighted interconnections based on diffractive optical elements for fixed-connection multilayer neural networks are investigated and compared in terms of propagation lengths, system volumes, connection densities, and interconnection cross talk. For a small overall system volume the limited-fan-out architecture can accommodate a much larger number of input and output nodes. However, the interconnection cross talk of the limited-fan-out space-variant architecture is relatively high owing to noise from the diffractive-optical-element reconstructions. Therefore a cross-talk reduction technique based on a modified design procedure for diffractive optical elements is proposed. It rearranges the reconstruction pattern of the diffractive optical elements such that less noise lands on each detector region. This technique is verified by the simulation of one layer of an interconnection system with 128 x 128 input nodes, 128 x 128 output nodes, and weighted connections that fan out from each input node to the nearest 5 x 5 array of output nodes. In addition to a significant cross-talk reduction, this technique can reduce the propagation length and system volume.     

All-optical stage of an omega network

All-optical multistage interconnection networks are desirable for overcoming the limitations of optical signal regeneration in switching systems. We present a new implementation of the perfect-shuffle interconnection pattern that is coupled with an all-optical switching element, forming a complete stage of a multistage network. Switching is performed with birefringent calcite crystals and a ferroelectric liquid-crystal device, while interconnection is achieved with a space-semivariant imaging configuration. Cascading the layout allows this system to be used to construct an all-optical multistage interconnection network. An experimental demonstration of the stage is presented.     

Node-based reconfigurable volume interconnections. 1. Principles and optical design

We present a general-purpose three-dimensional interconnection network that models various parallel operations between two data planes. This volume interconnection system exhibits reconfigurable capabilities because of parallel and externally weighted interconnection modules, called nodes. We propose a generic optical implementation based on the cascading of two planar hologram arrays, coupled with a bistable optically addressed spatial light modulator. The role of this component is discussed in terms of energy regeneration and spatial cross-talk limitation. As an example, a binary matrix-matrix multiplier is implemented that uses a ferroelectric liquid-crystal light valve.     

64-channel correlator implementing a Kohonen-like neural network for handwritten-digit recognition

We present an optical implementation of an improved version of the Kohonen map neural network applied to the recognition of handwritten digits taken from a postal code database. Improvements result from the introduction of supervision during the learning stage, a technique that also simplifies the map layer labeling. The experimental implementation is based on a frequency-multiplexed raster computer-generated hologram used to realize the required N(4) interconnection. The setup is shown to be equivalent to a 64-channel correlator. Computer simulations are used to study various detection and classification procedures. The results of the optical experiments, obtained with binary phase computer-generated holograms, are presented and shown to be in excellent agreement with the simulations.     

Folded free-space polarization-controlled multistage interconnection network

We present a folded free-space polarization-controlled optical multistage interconnection network (MIN) based on a dilated bypass-exchange switch (DBS) design that uses compact polarization-selective diffractive optical elements (PDOE's). The folded MIN design has several advantages over that of the traditional transparent MIN, including compactness, spatial filtering of unwanted higher-order diffraction terms leading to an improved signal-to-noise ratio (SNR), and ease of alignment. We experimentally characterize a folded 2 x 2 switch, as well as a 4 x 4 and an 8 x 8 folded MIN that we have designed and fabricated. We fabricated an array of off-axis Fresnel lenslet PDOE's with a 30:1 SNR and used it to construct a 2 x 2 DBS with a measured SNR of 60:1. Using this PDOE array in a 4 x 4 MIN resulted in an increased SNR of 120:1, highlighting the filtering effect of the folded design.     

Regular geometries for folded optical modules

We present three new three-dimensional right-cylindrical folded modular interconnection architectures. To compare these systems among each other and with earlier designs, we introduce several figures of merit. The figures of merit describe such aspects of the system as the compactness, the relative angles of the optical axis to optical elements in the system, and system manufacturability. These figures of merit permit the designer of such an optical system to choose the geometry best suited for a particular application.     

Elements of a hybrid interconnection theory

We present a textbooklike treatment of hybrid systems employing both optical and electrical interconnections. We investigate how these two different interconnection media can be used in conjunction to realize a system not possible with any alone. More specifically, we determine the optimal mix of optical and normally conducting interconnections maximizing a given figure-of-merit function. We find that optical interconnections have relatively little to offer if the optical paths are constrained to lie on a plane (such as in an integrated optics system). However, if optical paths are permitted to leave the plane, they may enable considerable increase in performance. In any event the prize in terms of performance is accompanied by a penalty in terms of system power and/or size.     

Packaged optical interconnection system based on photorefractive correlation

We present an experimental implementation of a packaged free-space optical interconnection system by photorefractive correlation. The system consists of a phase code, a LiNbO(3) crystal, two computergenerated-hologram Fourier-transform lenses, and a detector, all mounted on a glass substrate. We present experimental results with a prototype packaged system showing interconnections between 25 inputs and 25 outputs, and we discuss the possibility of applying this packaging technology to interconnections between larger arrays.     

Optical perfect-shuffle network implementation by use of an ordinary imaging system and holographic gratings

We describe an approach to achieve the optical perfect-shuffle interconnection network in an ordinary optical imaging system; a holographic grating is inserted in the proper position, and a corresponding spatial filter is inserted in its back focal plane. This approach is simple, and the space-bandwidth product of the optical system can be better utilized. As an experimental demonstration, the perfectshuffle interconnection network is shown in one and in two dimensions.     

Speed and energy analysis of digital interconnections: comparison of on-chip, off-chip, and free-space technologies

We model and compare on-chip (up to wafer scale) and off-chip(multichip module) high-speed electrical interconnections withfree-space optical interconnections in terms of speed performance andenergy requirements for digital transmission in large-scalesystems. For all technologies the interconnections are firstmodeled and optimized for minimum delay as functions of theinterconnection length for both one-to-one and fan-outconnections. Then energy requirements are derived as functions ofthe interconnection length. Free-space optical interconnectionsthat use multiple-quantum-well modulators or vertical-cavitysurface-emitting lasers as transmitters are shown to offer aspeed-energy product advantage as high as 30 over that of the electrical interconnection technologies.