738 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 46, NO. 6, JUNE 1998

ECI Value Generations in CSE-Based DistributorsJeong Gyu Lee,Member, IEEE, and Byeong Gi Lee,Fellow, IEEE

Abstract— In this letter we consider two efficient externalcontrol input (ECI) value generation methods for thecontrolledswitching element(CSE)-based distributor [1], which is a newdistributor structure that does not require the dummy addressgeneration and extraction operations of the conventional distrib-utors. The first method relies on the active packet counter and theECI generator for ECI value generation, and the second methodutilizes the intrinsic ECI generation property of the CSE-basedreverse banyan network(RBN). The first method brings forth aflexible distributor structure, while the second method renders avery simple structure. In fact, the second method yields the so-called autonomous distributor [2], consisting only of a CSE-basedRBN and a set of delays, which is perceived as the simplest amongall available distributors. In addition, we introduce a modifiedversion of the autonomous distributor which can speed up theconnection-state setup process.

Index Terms—ATM switch, packet concentrator, packet dis-tributor.

I. INTRODUCTION

I N FAST packet switching, a distributor refers to a devicethat can concentrate and distribute active packets entering

the input ports in cyclic fashion across the output ports. It findsa common usage in efficient buffer utilization [3]–[5]. Besides,it can be used in conjunction with 12 switching elementsfor constructing an asynchronous transfer mode (ATM) switchwith partially shared buffers [6] or it can be applied toconstructing a multichannel ATM switching structure withpreserved cell sequence [7].

As is well known, a distributor can be built out of thecombination of a running adder (RA), a reverse banyannetwork (RBN), and an additional register called thetail-of-queue (TOQ) register [3], [8]. Such a distributor structureis designed to route the incoming packets through dummyaddress generation, insertion, and extraction processes. Theseprocesses, however, increase the network operation speed dueto the resulting elongated packet length and increase thehardware complexity as well.

Recently, a new distributor structure that does not requirethe dummy address generation and extraction operation hasbeen proposed in [1]. The distributor is formed by an RBNconsisting ofcontrolled switching elements(CSE’s), a counter,an external control input(ECI) generator, and a TOQ register.

Paper approved by G. P. O’Reilly, the Editor for Communications Switch-ing of the IEEE Communications Society. Manuscript received February 20,1997; revised July 28, 1997. This paper was presented in part at the Asia-Pacific Conference on Communications, Osaka, Japan, June 1995.

J. G. Lee is with the Switching Methods Section, Switching TechnologyDivision, Electronics and Telecommunications Research Institute, Taejon 305-350, Korea (e-mail: leejg@etri.re.kr).

B. G. Lee is with the School of Electrical Engineering, Seoul NationalUniversity, Seoul 151-742, Korea (e-mail: blee@tsp7.snu.ac.kr).

Publisher Item Identifier S 0090-6778(98)04587-5.

The counter counts the incoming active packets and thecounted number is stored in the register. The ECI generator andthe register control the ECI’s of the CSE’s in the RBN so thatthe RBN can concentrate and route the incoming packets to thedesired output ports. The dummy address generation functionof the conventional distributor is replaced with the ECI valuegeneration function in this CSE-based distributor. Therefore,in the CSE-based distributor the ECI value generation processis a very essential part. As such, we set the goal of the letter indevising efficient ECI generation methods for the CSE-baseddistributor and examining the related structure changes.

In this letter we will introduce two ECI value generationmethods. The first method is for the original CSE-baseddistributor, including active packet counter and ECI generator.The second method is the one that takes the advantage of theintrinsic ECI value generation property of the CSE-based RBN[2]. We will discuss what property of CSE-based RBN rendersa new ECI value generation method, and how it impacts thestructure of the CSE-based distributor. In addition, we willintroduce a modified CSE-based RBN structure that can speedup the connection-state setup process by carrying it out inparallel fashion.

II. ECI GENERATOR-BASED GENERATION OF ECI VALUES

An -input CSE-based RBN is constructed from two-input RBN’s and a stage of CSE’s that are connected to

each other as illustrated in the dashed block of Fig. 1 (for).1 In this structure the connection-states of the front-

stage CSE’s are set in such a way that the even-sequencedactive packets get routed either to the upper or to the lower

-input RBN, depending on the ECI value .2 This actionforces the odd-sequenced active packets get routed to the other

-input RBN.According to [1], a CSE-based RBN can perform the

distribution function if assisted by a proper ECI value setting.More specifically, for an arbitrary input packet stream with

active packets coming into a CSE-based RBNwith input lines, there exists a unique set of ECI values

that maps the input stream into an output packet streamwith the active packets contiguously located at the desiredoutput ports, independently of the active input packet locationsand numbers. Therefore, the CSE-based RBN can performthe distribution function if the ECI values are appropriately

1An N -input RBN consists ofn stages of CSE’s and the ECI’sCi;j ; i =

0; 1; � � � ; n� 1; j = 0; 1; � � � ; 2i � 1; are labeled in such a manner that thefirst subscript indicates the stage number and the second subscript indicatesthe serial number of ECI’s within each stage. Refer to [1] for the circuitconfiguration of the CSE.

2In this letter we will follow the convention thatci;j denotes the value ofthe ECICi;j :

0090–6778/98$10.00 1998 IEEE

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 46, NO. 6, JUNE 1998 739

Fig. 1. CSE-based distributor with ECI generator [1](N = 8):

furnished in accordance with the desired distribution locations.Table I lists the set of ECI values for an eight-input CSE-baseddistributor that enables to distribute the active packets startingat the output port designated by the TOQ register value

The CSE-based distributor introduced in [1] relies on theECI generator and the active packet counter for packet dis-tribution, and has the overall structure depicted in Fig. 1.In this structure the ECI generator generates a pertinent setof ECI values according to the TOQ register value, andthe active packet counter provides the incoming active packetcount for use in updating the TOQ register value. Therefore,in the CSE-based distributor with active packet counter, theECI generator generates the ECI values assisted by the activepacket counter and the TOQ register.

The ECI generator can be constructed in a number ofdifferent ways. The most intuitive method is to employ amemory device to store the set of ECI values for all possibleTOQ values. By using the TOQ value as the memory address,we can read out a proper set of ECI values from the memory.Another simple method can be found in employing a set oflogic gates. For example, in the case, we can build theECI generator in Fig. 2(a), using Table I as the correspondingtruth table.

The ECI generator can also be constructed out of a shiftregister. If we compare the four columns for the ECI’s

– in Table I, which correspond to the last stage ECIvalues of the 8 8 distributor, then we find that a columnof ECI values is a circular-shifted version of any of theother three. Further, and can be generated out of

and through the relationsand , and, similarly, can be

generated out of and through the relationIn general, one can easily show, using the

intrinsic ECI value generation property to be described inthe following section, that the circular-shift property and therelation hold for andistributor with Taking advantage of these properties,we can construct a shift-register-based ECI generator, asexemplified in Fig. 2(b) for the 88 distributor. Each box

TABLE IECI VALUES SETTING FOR CSE-BASED DISTRIBUTOR (N = 8)

in the figure represents a flip-flop with the number insideindicating its initial logic value.3

III. A UTONOMOUS GENERATION OF ECI VALUES

In the CSE-based distributor the ECI values that should befurnished in the current time slot are uniquely determined bythe number of active packets arriving at the distributor up untilthe previous time slot. Further, the control output of a CSEin the CSE-based RBN indicates the modulo-2 sum of thenumber of active packets up to the current switching elementsplus the corresponding ECI values. So, it may be possibleto get the information that is needed to generate the set ofECI values for the next time slot from a set of control outputvalues in the current time slot. In this section we will examinethis relationship carefully, thereby devising a new CSE-baseddistributor structure.

We first define the following terms. For an-input CSE-based RBN, we call the group of CSE’s in thestage which are controlled by the ECI a switchingelement group(SEG), and denote it by In addition,we call the control output of the last CSE in eachSEG agroup control output(GCO), and denote the GCO ofSEG by Then, an SEG can be consideredas a generalized CSEhaving an ECI , a GCO ,and inputs and outputs

Now, we denote by andthe modulo- sum of the total number of active packetsarriving at the SEG up until the previous time slot and thecurrent time slot, respectively. Further, we denote the activitybit of input port by Then, the SEG satisfies thefollowing three equations for :

andif

andotherwise

(1)

(2)

and (3)

3Note that the ECI generation in this case is accomplished simply bytriggering the shift register to shift rightm times without regard to the TOQvaluek, which is made possible because the flip-flops store the informationon the previous TOQ register value.

740 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 46, NO. 6, JUNE 1998

(a) (b)

Fig. 2. ECI generators(N = 8): (a) Logic circuit-based ECI generator. (b) Shift-register-based ECI generator.

Based on the above expressions, we obtain the followingproperty, which holds between the GCO and the ECI in eachSEG of a CSE-based RBN.

Property 1: A CSE-based RBN performs a proper distribu-tion function if and only if each ECI value is set to beidentical to the corresponding GCO value of the previoustime slot, i.e., , where indicates the timeslot number.

Proof: We prove the “if” part only, since once it is done,the “only if” part holds accordingly due to the uniquenessproperty established in [1, Property 3].

For a simple notation, we put Then, at timeslot (i.e., ) indicates the modulo- value of the totalnumber of active packets arriving at the SEG up until theend of the previous time slot. If we denote by thenumber of active packets arriving at the SEG during timeslot , i.e., , then by (2)we have

Let be the TOQ register value obtained at the end of timeslot for the active packets arrived at thefront-stage SEG Then this implies that the TOQ valuewould have become if packets had arrived.In mathematical expression, this states that if

, then But sinceby (2), the latter expression

can be rewritten as This meansthat if is chosen identical to or, equivalently,

, then the first active packet arriving attime slot , with active packets readily arrived at time slot

, is routed to the th output buffer, incrementing the TOQvalue to Therefore, a proper packet distribution isdone for the ECI value taken as A similarreasoning applies to each SEG , thus establishing that aproper distribution is made for the ECI values ’s takenas forNote in this process that incrementing one active packet inSEG causes incrementing one active packet in only oneof SEG’s in the th stage without affecting other SEG’s.4

4As a consequence, exactlyn ECI values change at each increment ofactive packet number. We can confirm this using Table I, where exactly threeECI values change at each increment of the TOQ valuek:

Fig. 3. Autonomous distributor with rotational structure(N = 8):

This property yields a new type of CSE-based distributorin which the GCO in each SEG is connected to the ECI inseries with a time slot delay We call the resulting CSE-based distributor anautonomous distributor, as its ECI valuesare autonomously generated within the CSE-based RBN. Theresulting distributor therefore takes the rotational structureillustrated in Fig. 3 and can be considered as a distributorthat has a distributed implementation of the running adder andthe TOQ register of the conventional distributor. This novelstructure consists only of CSE’s and delay elements. Neitherthe active packet counter nor the ECI generator in Fig. 1are required in this structure. The autonomous distributor canbe reset whenever desired by resetting the delay elements,and it becomes a concentrator when the delay elements aredisconnected.

IV. A UTONOMOUS DISTRIBUTOR WITH

PARALLEL CONNECTION-STATE SETUP

The CSE-based RBN’s we have considered so far all rely onsequential processing for connection-state setup. That is, theconnection state of a CSE can be set up only after all of theconnection states of its upper CSE’s are determined. This caneasily be visualized by examining the dashed block of Fig. 1.

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(a) (b) (c)

Fig. 4. Illustration of sequential to parallel conversion of connection-state setup. (a) Front-stage SEG of the 8�8 autonomous distributor. (b) Divisioninto two subgroups. (c) Division into four subgroups.

As a consequence, the connection-state setup process could bea bottleneck in implementing a large-sized distributor. In fact,it takes XOR gate times, or , in completingthe connection-state setup of an-input SEG. This equallyapplies to the autonomous distributor also. Therefore, in thissection we consider how to curtail the connection-state setuptime.

The main source of long connection-state setup time in theCSE-based RBN is the serial connection of the ECI, whichflows downward through a series ofXOR gates. The CSE’sin the downstream have to wait until the message originatedfrom the ECI arrives, resulting in a long connection-state setuptime. Therefore, if we can modify the connection-state setupoperation such that it can be performed in parallel fashion byall CSE’s simultaneously, we can curtail the connection-statesetup time.

We now consider how to implement the above idea for eachSEG by following the procedure depicted in Fig. 4, for thefront-stage SEG of the eight-input autonomous distributor inFig. 3. If we split the SEG in Fig. 4(a) into two sub-SEG’sas shown in Fig. 4(b), then the GCO of the top sub-SEG’sbecomes , where denotes the number ofactive input packets arriving at the top sub-SEG. Therefore,if the GCO value can be calculated and given to the bottomsub-SEG as its ECI value in advance, then two sub-SEG’scan perform the connection-state setup process simultaneously.This is the basic idea of the parallel connection setup techniqueand Fig. 4(b) shows the resulting structure.5 Repeating thesame conversion procedure for the two sub-SEG’s in Fig.4(b), we obtain the four sub-SEG arrangement in Fig. 4(c). Ifwe apply this parallel connection setup technique to all otherstages in Fig. 3, we finally obtain the autonomous distributorstructure shown in Fig. 5. Note that each “switched CSE” inFig. 4 is replaced with amodified CSEand eachXOR subcircuitis simplified into atrijunction block T.

5Note that the parallel connection-state setup technique is similar in conceptto the carry look-ahead technique used in binary adders [9]. The modified SEGoperates such that each ECI is reset to logic zero while the active input packetsare being counted.

Fig. 5. Autonomous distributor with parallel connection-state setup capabil-ity (N = 8):

In the autonomous distributor with the parallel connection-state setup capability, each modified CSE counts the number ofactive input packets independently of the ECI to be applied toitself and reports the counted number to the adjacent trijunctionblock. Then the trijunction block collects the reported activepacket numbers and combines them together with the storedECI value to generate the new ECI values for each modifiedCSE. Therefore, the connection setup process is done inparallel among all of the modified CSE’s in the autonomousdistributor with parallel connection-state setup. Due to thisparallel processing, the connection-state setup time reducesto in the eight-input distributor. In general, the connection-state setup time reduces to for an -input SEG.

V. CONCLUDING REMARKS

In this letter we have introduced two new ECI generationmethods for the CSE-based distributor—the ECI generator-

742 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 46, NO. 6, JUNE 1998

based generation and the autonomous generation. The firstmethod uses an active packet counter and an ECI generatoras its essential components. The ECI generator itself can beimplemented either in the form of a lookup table or in adirect logic circuit. The advantage of this ECI generator-basedmethod is in its flexibility. That is, the CSE-based distributoremploying this method can be easily modified for otherfunctional purposes, whose example being the shift-sequencepermutation (SSP) network [1], [10]. The second method takesthe advantage of the intrinsic ECI generation property ofthe CSE-based RBN. The resulting autonomous distributorconsists of a CSE-based RBN and a set of delays only. Itdoes not require active packet counters or ECI generators and,therefore, it appears to be the simplest among all distributorsknown to us to date. In fact, this autonomous distributor isas simple as the iterative cell-based concentrator introducedin [11].

The autonomous distributor with the parallel connection-state setup capability that we have considered in the lastsection curtails the connection-state setup time of to

at the cost of incremental logic circuits, thusmaking the CSE-based distributor useful even in large-sizeddistribution applications. It is worth noting that the modifiedCSE element can be equally employed in the above-mentionedconcentrator for a fast connection-state setup.

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