Banyan Networks Research Articles

Dual banyan network (DBN) design: A quantum-dot cellular automata (QCA) based approach

The inputs use a non-blocking internal process to distribute the data using address of the port of the receiver using a non-blocking interior multistage transmission architecture known as a dual banyan network (DBN). The DBN is a primary component in many communication and switching applications because it efficiently routes and switches data packets. This study shows how to construct a single-layer DBN using QCA. A single layer 2 × 2 crossbar network (CBN) with two inputs and two outputs is suggested and developed in QCA to create the proposed communication architecture. In this study, a 2 × 2 CBN is used as a preliminary building block to create a 4 × 4 DBN. We present a detailed analysis of the DBN design, including its architecture, functionality, and performance evaluation. For a fault-free crossbar switch design, the consequence of a fault that affects the control line is noticed and surpassed. Similarly, the proposed architectures' fault tolerance has been described by considering fault scenarios at the 2 × 2 CBN control lines. Considering the logic gates, number of clock cycles, and device size complexity of the designs are measured. All of the designs were implemented using QCADesigner software. The power dissipation of the suggested layouts.

Necessary Conditions and Empirical Observations for Rearrangeable Banyan-Type Networks

A banyan-type network is constructed by aligning unit switches with two inlets and outlets in multiple stages. Rearrangeable banyan-type networks are crucial for applications such as communication systems because they can universally establish connections for any request without blocking. If the number of network inputs (or outputs) is 2^n (n > 0), the banyan-type network should have 2n − 1 or more stages to be rearrangeable. A few rearrangeable 2n − 1 stage networks have been reported. However, the class of rearrangeable 2n − 1 stage banyan-type networks has not been completely clarified. This study examines the identification of rearrangeable 2n − 1 stage banyan-type networks that are not isomorphic to one another. This is done by generating candidate networks and checking their rearrangeability via the satisfiability problem. The drawback of this approach is its poor scalability due to numerous candidates. To eliminate this drawback, it is shown that the candidates can be reduced to a smaller number of networks called pure banyan networks. This is achieved by analyzing network isomorphism. Next, necessary conditions are derived for rearrangeability. Utilizing the conditions, the number of candidate networks further decreases because blocking networks are identified and removed from the candidates. For the reduced number of candidate networks, rearrangeability is assessed through computer experiments for n = 4 and 5. For n = 4, the result shows that any rearrangeable configuration is isomorphic to previously reported rearrangeable networks. For n = 5, the blocking probability is extremely low and the rearrangeability is inconclusive for two groups of networks.

On a Symmetric Image Cryptosystem Based on a Novel One-Dimensional Chaotic System and Banyan Network

In this paper, a Banyan network with high parallelism and nonlinearity is used for the first time in image encryption to ensure high complexity and randomness in a cipher image. To begin, we propose a new 1-D chaotic system (1-DSCM) which improves the chaotic behavior and control parameters’ structure of the sin map. Then, based on 1-DSCM, a Banyan network, and SHA-256 hash function, a novel image encryption algorithm is conducted. Firstly, a parameter is calculated using SHA-256 hash function and then employed to preprocess the plaintext image to guarantee high plaintext sensitivity. Secondly, a row–column permutation operation is performed to gain the scrambled image. Finally, based on the characteristic of DNA encoding, a novel DNA mapping is constructed using an N=4 Banyan network and is used to diffuse the scrambled image. Simulation results show that the 1-DSCM has excellent performance in chaotic behavior and that our encryption algorithm exhibits strong robustness against various attacks and is suitable for use in modern cryptosystems.

A novel design of a dependable and fault-tolerant multi-layer banyan network based on a crossbar switch for nano communication

A novel design of a dependable and fault-tolerant multi-layer banyan network based on a crossbar switch for nano communication

Blocking performance of extended pruned vertically stacked optical banyan structure under different link failure conditions

The blocking performance of extended pruned vertically stacked optical banyan (VSOB) networks under different link failure conditions has been analyzed in this paper. We applied plane fixed routing with linear search and plane fixed routing with random search algorithms to route the optical data through the network in our simulation. Our simulation results show that adding one or two extra planes to the pruned VSOB network reduces the blocking probability significantly. Beyond two extra planes, the decrease of blocking probability is not so significant. A close approximation of the minimum number of planes required to make the extended pruned vertically stacked optical banyan networks nonblocking has been presented.

Performance enhancement of 8$$\times$$8 dilated banyan network using crosstalk suppressed GMZI crossbar photonic switches

Performance enhancement of 8$$\times$$8 dilated banyan network using crosstalk suppressed GMZI crossbar photonic switches

Blocking Probability Analysis for Optical Banyan Networks With Link Failure

Highly fault-tolerant optical switch is becoming a critical network element for large wavelength division multiplexing mesh networks. Optical nodes built on replicated banyan network (RBN) structures are attractive for serving as optical switching systems due to the nice properties of banyan network structures. Furthermore it is expected that an optical RBN structure also has a good fault-tolerant capability because it consists of multiple identical banyan networks. Previous analytical models have been developed to understand the blocking behaviors of optical RBN networks without taking into account the link failure in optical RBN networks. In this paper, we conduct the link failure-tolerant analysis of optical RBN networks and present an analytical model for the blocking probability of optical RBN networks when link failures are taken into account. The model is significant because it provides network developers a quantitative guidance to determine the effects of network failure on the overall blocking behaviors of optical RBN networks and enables a desirable tradeoff to be made between blocking probability and hardware cost in a faulty optical RBN network.

Design of single layer banyan network using quantum-dot cellular automata for nanocommunication

Banyan network is a multistage communication architecture that route the input signal based on port address of receiver. The port address is recognized as a string. This paper illustrates the design of a novel single layer banyan network using QCA for nanocommunication. To design the proposed communication architecture, a new single layer 2-inputs and 2-outputs crossbar switch is proposed and implemented in QCA. Using this crossbar switch as a major building block, a 4x4, and 8x8 banyan networks have been achieved in this paper. The effect of stuck-at-fault at the control input is observed and excelled for fault free design of the crossbar switch. Similarly, the fault tolerant nature of the proposed banyan networks have been characterized by considering the stuck-at-fault effect at the control signals of crossbar switches within the architecture. The designs are evaluated considering device area, delay, and logic gates. Theoretical values have been matched up with the simulation results to verify design accuracy.

Performance Analysis of $f$ -Cast Crosstalk-Free Optical Banyan Networks

Banyan networks serve as a class of important switching network architecture, whose multicast capability is critical for future high-performance switches to support multicast-intensive applications. The available literature indicates that, in order to construct optical multicast banyan networks based on the directional coupler (DC) technology, a high-hardware cost is usually involved to ensure the nonblocking property. In this paper, we conduct blocking probability analysis for such networks to explore the inherent tradeoff between blocking probability and hardware cost. In particular, we focus on a class of DC-based optical networks built on the replicated banyan network (RBN) architecture, and develop a theoretical upper bound on blocking probability for such networks under the general $f$ -cast traffic, which covers the unicast and multicast as special cases. This bound captures the overall blocking behavior of $f$ -cast optical RBN networks and agrees with the conditions of strictly nonblocking $f$ -cast optical RBN networks. The proposed bound is significant because it provides a fundamental guideline to achieve the desirable tradeoff between blocking probability and hardware cost. This paper shows that the hardware cost of an $f$ -cast optical RBN network can be dramatically reduced if a small blocking probability is allowed.

FPGA implementation of trellis decoders for linear block codes

Abstract. Forward error correction based on trellises has been widely adopted for convolutional codes. Because of their efficiency, they have also gained a lot of interest from a theoretic and algorithm point of view for the decoding of block codes. In this paper we present for the first time hardware architectures and implementations for trellis decoding of block codes. A key feature is the use of a sophisticated permutation network, the Banyan network, to implement the time varying structure of the trellis. We have implemented the Viterbi and the max-log-MAP algorithm in different folded versions on a Xilinx Virtex 6 FPGA.

Block-free optical quantum Banyan network based on quantum state fusion and fission

Optical switch fabric plays an important role in building multiple-user optical quantum communication networks. Owing to its self-routing property and low complexity, a banyan network is widely used for building switch fabric. While, there is no efficient way to remove internal blocking in a banyan network in a classical way, quantum state fusion, by which the two-dimensional internal quantum states of two photons could be combined into a four-dimensional internal state of a single photon, makes it possible to solve this problem. In this paper, we convert the output mode of quantum state fusion from spatial-polarization mode into time-polarization mode. By combining modified quantum state fusion and quantum state fission with quantum Fredkin gate, we propose a practical scheme to build an optical quantum switch unit which is block free. The scheme can be extended to building more complex units, four of which are shown in this paper.

Modular Architectures of Multistage Switching Networks

This paper defines a procedure for designing the architecture of multistage switching networks. Our proposal is the result of a systematic study of the properties of multistage networks on one side and of optical switching systems on the other side. Modularity of the implementation is the primary concern, allowing the construction of a generic-size fabric by the simple cascading of multiple-stage modules. In this paper, we show in detail the application of the approach to a family of banyan networks, although the method can be extended to other types of networks. The designed architecture can be exploited for various implementation technologies, for instance, integrated optics and free-space optics. The method can even be applied to electronic VLSI/ULSI circuits. After presenting the design procedure, we discuss practical implementations in different technology scenar- ios. The main contribution of this paper is to simplify the building of large switches by cascading a number of switching modules that combine the internal stage architecture with the interconnection between stages.

Permutation Network for Reconfigurable LDPC Decoder Based on Banyan Network

Since the structured quasi-cyclic low-density parity-check (QC-LDPC) codes for most modern wireless communication systems include multiple code rates, various block lengths, and the corresponding different sizes of submatrices in parity check matrix (PCM), the reconfigurable LDPC decoder is desirable and the permutation network is needed to accommodate any input number (IN) and shift number (SN) for cyclic shift. In this paper, we propose a novel permutation network architecture for the reconfigurable QC-LDPC decoders based on Banyan network. We prove that Banyan network has the nonblocking property for cyclic shift when the IN is power of 2, and give the control signal generating algorithm. Through introducing the bypass network, we put forward the nonblocking scheme for any IN and SN. In addition, we present the hardware design of the control signal generator, which can greatly reduce the hardware complexity and latency. The synthesis results using the TSMC 0.18 μm library demonstrate that the proposed permutation network can be implemented with the area of 0.546 mm 2 and the frequency of 292 MHz.

Distributed Control Routing Algorithms for Rearrangeably Nonblocking Optical Banyan Networks

Optical banyan networks can be made rearrangeably nonblocking using its multiple copies in unison. Such rearrangeably nonblocking networks are known as vertically stacked optical banyan (VSOB) networks. Centralized control routing algorithm for this rearrangeably nonblocking optical banyan networks has time complexity O ( N log2 N ). A distributed control routing algorithm with time complexity O (log2 N ) has been proposed recently in which authors have considered N completely connected processors to take routing decision which practically would be very difficult to implement for large N . In this paper we propose two distributed control routing algorithms where processors are loosely connected. In the first algorithm ) ( N O processors work in pipelined fashion, and take the routing decision in linear time. In the second algorithm N inputs synchronously hunt for a free route among ) ( N O copies of a banyan network using a look up table. This algorithm has time complexity ) ( N O . Also the processors do not need to be completely connected, which makes it more practical for implementation.

The deflection self-routing Delta network: a dynamically fault-tolerant high-radix multistage interconnection network

High-radix multistage interconnection networks are popular interconnection technologies for parallel supercomputers and cluster computers. In this paper, we presented a new dynamically fault-tolerant high-radix multistage interconnection network using a fully-adaptive self-routing. To devise the fully-adaptive self-routing for recovering the misrouting around link faults in such network, we introduce an abstract algebraic analysis of the topological structure of the high-radix Delta network. The presented interconnection network provides multiple paths by using all the links of all the stages of the network. We also present a mathematical analysis of the reliability of the interconnection network for quantitative comparison against other networks. The MTTF of 64×64 network proposed is 2.2 times greater than that of the cyclic Banyan network. The hardware cost of the proposed network is half that of the cyclic Banyan network and the 2D ring-Banyan network.

Upper Bound on Blocking Probability for Vertically Stacked Optical Banyan Networks with Link Failures and Given Crosstalk Constraint

Vertical stacking of multiple copies of an optical banyan network is a novel scheme for building nonblocking optical switching networks. The resulting network, namely vertically stacked optical banyan (VSOB) network, preserves all the properties of the banyan network, but increases the hardware cost significantly under first order crosstalk-free constraint. However, stringent crosstalk constraint may not always be necessary. Considering the fact that some designer may want to compromise the blocking probability and crosstalk constraint to a certain degree with the hardware cost, blocking behaviour of such VSOB networks have been analyzed to studying network performance and finding a graceful compromise between hardware costs and blocking probability under or without crosstalk constraint. In this paper, we present the simulation results for upper bound on blocking probability of VSOB networks with link failures and given degree of crosstalk constraint. We show how crosstalk adds a new dimension to the performance analysis on a VSOB networks. The simulation results presented in this paper can guide network designer in finding the trade-off among the blocking probability, the degree of crosstalk and the hardware cost in terms of vertical copies of banyan network in the presence of link failures.Keywords: Banyan networks; Blocking probability; Vertical stacking; Link-failures; Crosstalk.© 2009 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.DOI: 10.3329/jsr.v1i3.1191 J. Sci. Res. 1 (3), 484-494 (2009)

Blocking probability analysis of pruned optical banyan networks on vertical stacking scheme with extra banyan planes

Vertically stacked pruned optical banyan networks with extra planes (in short, EP-VSOB networks) have lower switch count and optimal time complexity (O(log2N)) for routing N input requests. However, blocking probability is relatively higher than that of a VSOB networks using regular banyan planes. In the EP-VSOB architecture, the number of pruned planes has always been considered as N, and a few extra planes (regular banyan) have been added with these pruned planes. In this paper we present the results of blocking analysis of a more generalized architecture in which the number of pruned planes can be 2x, where x⩾0 in addition to the variable extra planes. This generalization helps us make a compromise between different constraints and performance metrics. Our simulation results show that for some given performance requirements (e.g. cost, speed or blocking probability) we can choose a network that has lower switch count compared to N-plane pruned crosstalk-free optical banyan networks. For example, to ensure blocking probability <0.02, previously we would chose a pruned network of 32 pruned planes and 1 extra planes (a regular banyan); however, our simulations results show that a network of 16 pruned planes and 2 extra planes is enough to ensure the same performance. It is notable that, the hardware cost decreases by 28.65% in this new combination of pruned and extra planes. We believe our results will provide more flexibility in choosing a particular EP-VSOB network satisfying given requirements.

On Number of Planes of Rearrangeably Nonblocking Optical Banyan Networks with Link Failures

Vertically stacked optical banyan (VSOB) networks are attractive for serving as optical switching systems due to the desirable properties (such as the small depth and self-routing capability) of banyan network structures. Although banyan-type networks result in severe blocking and crosstalk, both these problems can be minimized by using sufficient number of banyan planes in the VSOB network structure. The number of banyan planes is minimum for rearrangeably nonblocking and maximum for strictly nonblocking structure. Both results are available for VSOB networks when there exist no internal link-failures. Since the issue of link-failure is unavoidable, we intend to find the minimum number of planes required to make a VSOB network nonblocking when some links are broken or failed in the structure. This paper presents the approximate number of planes required to make a VSOB networks rearrangeably nonblocking allowing link-failures. We also show an interesting behavior of the blocking probability of a faulty VSOB networks that the blocking probability may not always increase monotonously with the increase of link-failures; blocking probability decreases for certain range of link-failures, and then increases again. We believe that such fluctuating behavior of blocking probability with the increase of link failure probability deserves special attention in switch design.  Keywords: Banyan networks; Blocking probability; Switching networks; Vertical stacking; Link-failures. © 2009 JSR Publications. ISSN: 2070-0237(Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v1i1.1070

Rearrangeable f-cast multi-log2 N networks

Multi-log2 N networks (or vertically stacked banyan networks) have been an attractive class of switching networks due to their small depth O(log N), absolute signal loss uniformity and good fault tolerance property. Recently, F.K.Hwang extended the study of multi-log2 N networks to the general f-cast case, which covers the unicast case (f = 1) and multicast case (f = N) as special cases, and determined the conditions for these networks to be f-cast strictly nonblocking when the fan-out capability is available at both the input stage and middle banyan stage. In this paper, we study the rearrangeable f-cast multilog2 N networks under both node-blocking scenario (relevant to photonic switches) and link-blocking scenario (relevant to electronic switches). In particular, we consider the following three fan-out cases in our study: (1) no restriction on fan-out capability; (2) input stage has no fan-out capability; (3) middle banyan stage has no fan-out capability. We determine the necessary conditions for the first two cases while obtaining the necessary and also sufficient condition for the third one.

Optical implementation of rearrangeable nonblocking double banyan interconnection network in free space

The banyan network plays an important role in optical interconnection networks. A smart and compact double banyan network with cascading banyan network and inverse banyan network is proposed by using a polarizing beam-splitter (PBS), a phase spatial light modulator (PSLM), a half-wave plate (HWP), a double-faced reflective mirror (DFRM), and mirrors. The PBS features that the s-component (perpendicular to the incident plane) of the incident light beam is reflected, and the p-component (parallel to the incident plane) passes through it. Simultaneously, the bipartition graph algorithm (BGA) is adopted to ascertain the state of the node switch in each node stage (straight or crossover connection). According to switching logic, under control of external electrical signals, the PSLM functions to control routing paths of the signal beams, i.e. the polarization of each optical signal is rotated or not rotated 90° by a programmable PSLM. Since the proposed optical setup consists of only optical polarization elements, it is compact in structure, and possesses a low energy loss, a high signal-to-noise ratio and an available large number of optical channels. Finally, the discussions and the experimental results show that the double banyan network proposed here, owing to without signal blocking and conflict, may be used in optical communication and optical information processing.