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

A Fast CRC Toolation on FPGA Using a Pipelined Edifice coercion the Polynomial Non-location 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 hallucination challenge is a very niggardly agency on telecommunication applications. The disconnection towards increasing axioms objurgates requires aggravate and aggravate sofisticated toolations. In this article, we introduce a manner to tool the CRC agency established on a pipeline constituency coercion the polynomial non-location.It corrects very conducively the despatch exploit, allowing axioms objurgates from 1 Gbits/s to 4 Gbits/s on FPGA toolions, according to the analogousisation flatten (8 to 32 morsels).
1 INTRODUCTION The CRC (Cyclic Redundancy Checking) codes are rightd in a chance of telecommunication applications. They are rightd in the inside layers of protocols such as Ethernet, X25, FDDI and ATM (AAL5). However, on modem networks, the insufficiency coercion increasing axioms objurgates (aggravate 1 Gbit/s) is elucidation the businesss on exploit very excellent. Indeed, the despatch amendment (conspicuous clock objurgates) ascribable to the technological disconnection is insufficient to apportion the require.Consequently, odd edifices must be bequeathed. Targetting the applications to an FPGA cognizance is an offspring coercion this article, as it allows dejected-cost intentions. The sickly and plum serial toolation is a augustan hardware toolation of the CRC algorithm.
Unfortunatly, on an FPGA toolation with maximal clock quantity of 250 MHz, maximal axioms objurgate is scant to 250 Mbits/s is the best circumstance. Excellenter axioms objurgates can solely be obtained through analogousisation. Some analogous edifices entertain been incomplete in the elapsed to address the insufficiency coercion excellent axioms throughput [ 1][2].The deep substance is usually to period the rapidly increasing area aggravatehead conjuncture suiconsultation the despatch exploit. In this article, we introduce a analogous way coercion the polynomial non-location established on a pipeline constituency. The analogousisation can be led to any flatten and is solely lim- ited by the area business fixed on the intention. The axioms throughput is approximately promptly linked to the analogousisation flatten, as the maximal clock objurgate is referable attribuconsultation attribuconsultation attribuconsultation very sentient to it.

2 PRINCIPLE The polynomial non-location is the essential agency of the CRC applications.The serial toolation of the non-location is semblancen in emblem 1 coercion the circumstance where the polynomial divisor is G ( X ) = Go + G1. X1 + Gz. X2 + G3. X3 = 1 + X + X 3 . As implied priorly, the axioms throughput of this serial toolation is truly dejected. Very excellent axioms objurgates can solely be achieved with excellent clock frequencies, which in metamorphose can solely be obtained using rather valuable technological disentanglements.
Analogousisation of axioms mannering is the deep disentanglement to correct the despatch exploit of a tour (or plan) if the clock objurgate must redeep dejected.Pipelining may be rightd as an conducive analogousisation manner when a repeatitive manner must be applied on wide volumes of ‘data. Prior works entertain addressed the analogousisation substance in wide requireing computational applications, in-particular in arithmetic (eg. [3][4]) and hallucination restrain coding tours (eg. [11[21[61). In the serial edifice (emblem I), a odd axioms morsel is inject on each clock cycle. The prior cumulated accrueder is conjointly numerous by X and separated by G(z) (where G(z) is the polynomial divisor).
On P Emblem I : Serial polynomial non-location coercion G ( X ) = 1 -tX + X 3 -7803-7057-0/01/$10. 00 02001 IEEE. 1231 successive clock cycle , P morsels are injected and P successive reiter-ation and non-locations are effected. The contiguous coercionmula (cognate to the sample of emblem 1) describes the agency effected on uncompounded clock cycle. 0 T = [ o o 1 !]=[n Gz 0 1 o 1 1 Go GI 0 i ] 0 3 RESULTS This edifice entertain been tooled on FPGA cognizances of the FLEXlOKE ALTERA nativity. These cognizances entertain their maximal clock quantity scant to 250 MHz. The edifice was tested on the generating polynomials of consultation 1.
The consequences in consultation 2 were obtained on FPGA cognizances of the FLEXlOKE ALTERA nativity.The edifice tested in these samples tools a amply agencyal CRC checker. The synchronisation signals to transcribe and recognize axioms appertainingly on input and ouput are amply tooled. The cem was duncompounded using Synplify 5. 3 and MaxPlus11 10. 0. The edifice was tested coercion 3 contrariant flattens of paralelism on 6 contrariants exemplar divisor polynomials.
It can be referable attribuconsultation attributableiced that G17(z) is rightd on ethernet, FDDI and AALS-ATM, conjuncture G14(z) is the exemplar polynomial coercion the X2. 5 protocol. The clock objurgates must be compared to the excellentest quantity (250 MHz) that can be effected on FLEXlOKE cognizances.The “IC” sign instrument “logical cells” and is an sign of the area expenditure. The consequences must be compared to those obtained in [SI. A axioms objurgate of 160 Mbits/s was obtained on an ALTERA FLEXIOK cognizance (max. clock objurgate of 125 MHz), on a 32-morsel analogous CRC runtime-configurable toolation of the decoder, established on the right of analogous combi- A pipeline constituency can be bequeathed by the toolation of P successive reiter-ations and non-locations.
However, to tend the clock objurgate excellent, the P agencys should referable attribuconsultation attribuconsultation attribuconsultation be duncompounded in a uncompounded combinatorial obstruct. Thus, the qualitys of the P-multiplingldivising obstruct must be separated by records.This is the basic conception of the pipeline constituency. Each of the P analogous morsels of an input must be injected in their appertaining pipeline quality. accordingly, they must be injected on contrariant clock cycles. This may be duncompounded if the morsels are advanced in a change-record constituency and (cf. the change record footfootfootpath among [ d i n o ,.
.. , [douto, … ,doutp-l] in the emblem 2, with P = 8 in this sample and G ( X ) = 1 + X + X 3 . The agency effected when latter from the quality k + l to the quality k of the pipeline (k>O) is feeling in the contiguous coercionmula, where G ( X ) = 1 + X + X 3 as it is in emblem 2.
ith Ri,J= 0 wheni + j > p – 1. The P morsels of an input are mannered in P clock cycles. At each clock cycle, the consequence of the mannering of P morsels is adapted at the quenchedput of the pipeline constituency. This consequence (the accrueder of the P morsels separated by G(z) must be cumulated in the [ROO, ROZ] ROI, record using a returning way, homogeneous to the intent of the serial edifice of emblem 1. The cumulated accrueder at date t must be numerous by X p and then separated by G(x). Then, the odd inequiconsultation accrueder hereafter quenched of the pipeline constituency can be cumulated. This manner is describet in the contiguous coercionmula.
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 obstruct coercion the polynomial non-location as introduceed in [ 11. The compel obtained on the 32-morsel analogous edifice is among 16 and 30 dates, that is, 8 to 1. 5 dates using the identical technology (cf. consultation 2). Coercion any concert of the intention parametres, the latency is alway resembling to P clock cycles where P denotes the analogousisation flatten. It can be referable attribuconsultation attributableiced that coercion attached a maximal polynomial divisor mark, the area expenditure (estimate of logic cells ) is approximately proportional to the analogousisation flatten of the edifice.Furthermore, the consequences semblance that a wide extension of the analogousisation flatten can be duncompounded with a unintoxicated lower of maximal clock quantity.
The delicate footfootfootpath is ascribable to the M matrix. The complication of this matrix depends on the choosen polynomial (estimate and lie of the non-zero stipulations in the polynomial). It to-boot depends on the analogousisation 1232 flatten, barring referable attribuconsultation attribuconsultation attribuconsultation linearly. Actually, a excellenter analogousisation flatten can direct to a short involved matrix.

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