Optical TDM Sorting Networks for

\Sunshine: A high peformance self-routing broadband packet switch architecture," Proc. 17] M. Kondo, et al., \High-speed optical time switch with integrated optical 1 4 switches and single polarization ber delay lines," Technical Digest, Intl. \Serial array time slot inter-changers and optical implementations, 25 Both networks preserve frame integrity and can handle synchronous TDM input streams. The proposed multichannel time slot sorters, by virtue of sorting TDM inputs without expanding into a space fabric, prove more economical than typical sorters used in sort-banyan networks. Thus the proposed sorters form a generalization of traditional sorting networks and can form the basis for space-time division switches with TDM inputs, where each time slot in an input frame represents a distinct user. \An experimental photonic time-slot interchanger using optical bers as reentrant delay-line memories," J. 24 For the multichannel time slot sorter B F L;J 23], using 22 optical switches and feed forward delay lines, we have, sw(B F L;J) = L 2 (jl + j(j + 2) + l(l + 1) 2): (34) Comparing the number of switches for CRM L;J with the number of switches for B L;J , we get, Similarly comparing the number of switches for CRM L;J with the number of switches for For example the diierence in the number of switches between CRM 1024;1024 and B F 1024;1024 is 9262 optical switches, which would be a considerable saving in cost. The frame delay for CRM L;J , computed using the formulae in the previous section, is, D(CRM L;J) = J(j 2 + 3j + 2) 4 : (37) A comparison between the switch counts and frame delays of the two multichannel time slot sorters RM L;J and CRM L;J yields the following interesting result: (39) Equations 38 and 39 illustrate the space-time tradeoos beteen the two architectures, where a reduction in hardware complexity for CRM L;J is acheived by paying a penalty in terms of increased frame delay. 5 Conclusions We have proposed two multichannel time slot sorters based on odd-even merge sort, which use 2 2 optical switches and ber delay lines connected in a feed forward fashion. One of the sorters has less frame delay but more number of switches than the other, and vice versa. 23 sorted sequences arranged in column major order within row pair. Adjacent columns of each sequence are separated by J=K columns in the input matrix). Then, we have,