“Optoelectronic Implementation of Multistage Interconnection Networks”

by Lily Cheng

August 1992

Communication between signal channels in parallel computing and telecommunication switching systems is accomplished by interconnection networks. With the increasing demand for solving computation-intensive tasks such as image processing, image understanding and telecommunication management, an interconnection network having high throughput is desirable. A 3-D

network which occupies a physical volume in space and interconnects a 2-D array of channels or processing elements to another is a promising candidate for such applications. The implementation of such 3-D networks must have high temporal and spatial bandwidth to achieve the high throughput requirement.

The problems of electrical interconnections such as crosstalk, clock skew, pin-in/pin-out and delays, limit the application of electronic technology to a 3-D network. On the other hand, optics has inherent 3-D properties, high bandwidth, parallelism in processing and input/output, and a low degree of interaction between the channels. All these properties make optics a good candidate for implementing 3-D networks. However, because it is very difficult for photons to interact with photons, it is difficult to have logic gates implemented optically. A possible approach is to utilize the capabilities of both optics and electronics in a 3-D network, but many questions remain. From the designer's point of view, there are questions of how to design a useful network structure, how to use them for different applications, and how to simplify the hardware complexity. From the builder's point of view, there are questions of how to use these two technologies efficiently, how to design and implement each component, and how to optimize the performance. This thesis attempts to answer these questions and to demonstrate ways of doing so.

We concentrate on a special type of 3-D multistage network, called Omega (shuffle/exchange) network. This network is composed of stages of shuffling on a square array of channels as fixed interconnections combined with dynamic switch elements at each stage. We discuss an optically efficient implementation of the shuffling operation on 2-D arrays. This method is called the one-copy algorithm and achieves 100% light power utilization theoretically as opposed to conventional methods which achieve only 25% efficiency. We have systematically developed the algorithm and have extended it to general types of shuffles. Optical 2-D shuffles using this method can be implemented by a hologram containing four facets. We experimentally built a holographic system to demonstrate this algorithm.

The 2-D version of this shuffle/exchange network, where shuffling is performed on an 1-D vector of channels, has been demonstrated to be equivalent to other multistage networks and has been studied in depth. We discuss the construction of various 3-D shuffle/exchange networks, and investigate their properties and relations to the 2-D networks. By doing so, we automatically understand what components are necessary and how to use various network structures in different applications. A complete mathematical discussion is provided. We design the optoelectronic dynamic switch element systematically by considering its functional structure, signal modulation techniques, and practical implementation issues. A prototype of one of the designs has been built from discrete components.

Because the 3-D shuffle/exchange network contains multiple stages, the hardware for both shuffling and switching in one stage must be duplicated log2N times to make the network full access, where N is the number of channels in the square array. We propose a method to spatially arrange the channels such that a single set of optics are used for 2-D shuffles for all the stages and the design of switch elements is simplified. The resulting system requires a feedback system and is an example of a space multiplexed optical multistage network. We discuss the channel arrangement, the feedback system, and the complexity issue for this space multiplexed architecture. Experimental results are presented.