# A Fast Crc Implementation on Fpga Using a Pipelined Architecture for the Polynomial Division

A Fast CRC Utensilation on FPGA Using a Pipelined Erection restraint the Polynomial Resistance Fabrice MONTEIRO, Abbas DANDACHE, Amine M’SIR,Bernard LEPLEY LICM, University of Metz, SUPELEC, Rue Edouard Belin, 57078 Metz Cedex phone: +33(0)3875473 11, fax: +33(0)387547301, email: fabrice. [email protected] org ABSTRACT The CRC blunder aggravatethrow is a very base character on telecommunication applications. The separation towards increasing axioms scolds requires spent and spent sofisticated utensilations. In this tract, we give a mode to utensil the CRC character grounded on a pipeline constitution restraint the polynomial resistance.It mends very effectually the expedite work, allowing axioms scolds from 1 Gbits/s to 4 Gbits/s on FPGA utensilions, according to the congruousisation plane (8 to 32 pieces).

1 INTRODUCTION The CRC (Cyclic Redundancy Checking) codes are portraitured in a hazard of telecommunication applications. They are portraitured in the interior layers of protocols such as Ethernet, X25, FDDI and ATM (AAL5). However, on modem networks, the claim restraint increasing axioms scolds (aggravate 1 Gbit/s) is contrast the employments on work very haughty. Indeed, the expedite advancement (eminent clock scolds) due to the technological separation is feeble to agree the claim.Consequently, odd erections must be bequeathed. Targetting the applications to an FPGA emblem is an progeny restraint this tract, as it allows mean-cost intentions. The sickly and obvious serial utensilation is a pure hardware utensilation of the CRC algorithm.

Unfortunatly, on an FPGA utensilation with maximal clock quantity of 250 MHz, maximal axioms scold is poor to 250 Mbits/s is the best contingency. Haughtyer axioms scolds can simply be obtained through congruousisation. Some congruous erections accept been projected in the spent to oration the claim restraint haughty axioms throughput [ 1][2].The ocean tenor is usually to proviso the fast increasing area aggravatehead period graceful the expedite work. In this tract, we give a congruous congruousity restraint the polynomial resistance grounded on a pipeline constitution. The congruousisation can be led to any plane and is simply lim- ited by the area employment be on the intention. The axioms throughput is closely straightway linked to the congruousisation plane, as the maximal clock scold is referable very impressible to it.

2 PRINCIPLE The polynomial resistance is the essential deed of the CRC applications.The serial utensilation of the resistance is appearancen in aspect 1 restraint the contingency where the polynomial divisor is G ( X ) = Go + G1. X1 + Gz. X2 + G3. X3 = 1 + X + X 3 . As implied controlegoingly, the axioms throughput of this serial utensilation is truly mean. Very haughty axioms scolds can simply be achieved with haughty clock frequencies, which in metamorphose can simply be obtained using rather rich technological disintegrations.

Congruousisation of axioms waying is the ocean disintegration to mend the expedite work of a tour (or contrivance) if the clock scold must reocean mean.Pipelining may be portraitured as an effectual congruousisation mode when a repeatitive way must be applied on capacious volumes of ‘data. Controlegoing works accept orationed the congruousisation tenor in capacious claiming computational applications, specially in arithmetic (eg. [3][4]) and blunder manage coding tours (eg. [11[21[61). In the serial erection (aspect I), a odd axioms piece is inject on each clock cycle. The controlegoing cumulated tarryder is unitedly multigenous by X and disconnected by G(z) (where G(z) is the polynomial divisor).

On P Aspect I : Serial polynomial resistance restraint G ( X ) = 1 -tX + X 3 -7803-7057-0/01/$10. 00 02001 IEEE. 1231 successive clock cycle , P pieces are injected and P successive teeming and resistances are executed. The proximate restraintmula (allied to the specimen of aspect 1) describes the deed dundisconnected on undisconnected clock cycle. 0 T = [ o o 1 !]=[n Gz 0 1 o 1 1 Go GI 0 i ] 0 3 RESULTS This erection accept been utensiled on FPGA emblems of the FLEXlOKE ALTERA parentage. These emblems accept their maximal clock quantity poor to 250 MHz. The erection was tested on the generating polynomials of board 1.

The fruits in board 2 were obtained on FPGA emblems of the FLEXlOKE ALTERA parentage.The erection tested in these specimens utensils a capaciously deedal CRC checker. The synchronisation signals to transcribe and decipher axioms appertainingly on input and ouput are capaciously utensiled. The construction was dundisconnected using Synplify 5. 3 and MaxPlus11 10. 0. The erection was tested restraint 3 opposed planes of paralelism on 6 opposeds model divisor polynomials.

It can be referableiced that G17(z) is portraitured on ethernet, FDDI and AALS-ATM, period G14(z) is the model polynomial restraint the X2. 5 protocol. The clock scolds must be compared to the haughtyest quantity (250 MHz) that can be dundisconnected on FLEXlOKE emblems.The “IC” symptom resources “logical cells” and is an symptom of the area waste. The fruits must be compared to those obtained in [SI. A axioms scold of 160 Mbits/s was obtained on an ALTERA FLEXIOK emblem (max. clock scold of 125 MHz), on a 32-piece congruous CRC runtime-configurable utensilation of the decoder, grounded on the portraiture of congruous combi- A pipeline constitution can be bequeathed by the utensilation of P successive teemings and resistances.

However, to frequent the clock scold haughty, the P deeds should referable be dundisconnected in a only combinatorial stop. Thus, the extents of the P-multiplingldivising stop must be disjoined by memorials.This is the basic purpose of the pipeline constitution. Each of the P congruous pieces of an input must be injected in their appertaining pipeline extent. therefore, they must be injected on opposed clock cycles. This may be dundisconnected if the pieces are deceased in a displace-register constitution and (cf. the displace register method betwixt [ d i n o ,.

.. , [douto, … ,doutp-l] in the aspect 2, with P = 8 in this specimen and G ( X ) = 1 + X + X 3 . The deed dundisconnected when passing from the extent k + l to the extent k of the pipeline (k>O) is picturesquely in the proximate restraintmula, where G ( X ) = 1 + X + X 3 as it is in aspect 2.

ith Ri,J= 0 wheni + j > p – 1. The P pieces of an input are wayed in P clock cycles. At each clock cycle, the fruit of the waying of P pieces is profitable at the quenchedput of the pipeline constitution. This fruit (the tarryder of the P pieces disconnected by G(z) must be cumulated in the [ROO, ROZ] ROI, register using a periodic congruousity, congruous to the contrivance of the serial erection of aspect 1. The cumulated tarryder at space t must be multigenous by X p and then disconnected by G(x). Then, the odd peculiar tarryder hereafter quenched of the pipeline constitution can be cumulated. This way is describet in the proximate restraintmula.

Ro,o,ROJ,R0,Sltfl = [Ro,o,RO,l,R0,zIt * M +[Ri,o, Ri,i, Rl,z]t * T f [Do,P-l, 0,Olt natorial stop restraint the polynomial resistance as giveed in [ 11. The constitute obtained on the 32-piece congruous erection is among 16 and 30 spaces, that is, 8 to 1. 5 spaces using the corresponding technology (cf. board 2). Restraint any cabal of the intention parametres, the latency is alway correspondent to P clock cycles where P denotes the congruousisation plane. It can be referableiced that restraint loving a maximal polynomial divisor class, the area waste (reckon of logic cells ) is closely proportional to the congruousisation plane of the erection.Furthermore, the fruits appearance that a capacious extension of the congruousisation plane can be dundisconnected with a reasonable abate of maximal clock quantity.

The discriminating method is due to the M matrix. The perplexity of this matrix depends on the choosen polynomial (reckon and lie of the non-zero conditions in the polynomial). It besides depends on the congruousisation 1232 plane, excluding referable linearly. Actually, a haughtyer congruousisation plane can bring to a close abstruse matrix.

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